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# Elite academic brokers: Professional Writing Service

## Sitemaps
[XML Sitemap](https://www.eliteacademicbrokers.com/sitemap_index.xml): Includes all crawlable and indexable pages.

## Posts
- [How to Land an Internship: A Step-by-Step Guide for Students](https://www.eliteacademicbrokers.com/how-to-land-an-internship/): "I don't have enough experience." "Every internship posting wants someone who already has one." "My résumé looks empty." "I don't even know where to start looking." "I've applied to a dozen internships and heard nothing back."
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- [Why Didn’t They Teach Us Emotional Intelligence in School? Essential Life Skills for Everyday Life](https://www.eliteacademicbrokers.com/emotional-intelligence-for-everyday-life/): This is the idea at the center of Why Didn't They Teach Me This in School? Emotional Intelligence for Everyday Life  the simple but important recognition that emotional intelligence is a learnable skill set, not a fixed personality trait, and it's one most of us have had to pick up the hard way, through trial, error, and experience.
- [Nursing School Time Management Tips: How to Stay on Track](https://www.eliteacademicbrokers.com/nursing-school-time-management/): Good nursing school time management comes down to a few habits: knowing what needs to be done, knowing when it needs to be done, breaking large tasks into smaller steps, protecting study time, and reviewing your priorities regularly. None of this requires a complicated system. It just requires a consistent one, which is exactly what this guide walks through.
- [How to Organize Nursing Assignments: A Practical Guide for Students](https://www.eliteacademicbrokers.com/how-to-organize-nursing-assignments/): It's a familiar scene: a care plan due Thursday, a discussion post due Friday, a case study due next Monday, and clinicals in between. On top of that, there's reading to finish and an exam to study for. Trying to keep all of it straight in your head usually means something gets missed. Remembering deadlines isn't a real system. Once you have more than two or three assignments running at once, you need somewhere to see everything at a glance, and a way to decide what to work on next. This guide walks through a practical, step-by-step approach to organizing nursing assignments that you can start using today, no special apps or complicated methods required.
- [Nursing Student Planner: How to Stay Organized and Study Smarter](https://www.eliteacademicbrokers.com/nursing-student-planner/): That's where a nursing student planner comes in. Instead of spreading your semester across sticky notes, phone reminders, and half-finished to-do lists, a nursing-specific planner brings your classes, clinicals, assignments, and study time into one system you can actually follow. It isn't about adding more to your plate. It's about seeing everything in one place, so nothing catches you off guard.
- [Best Side Hustles for College & University Students: A Practical Guide](https://www.eliteacademicbrokers.com/side-hustles-for-college-students/): Between classes, assignments, exams, part-time jobs, and whatever social life you can squeeze in, college life doesn't leave a lot of spare hours. Add rent, textbooks, groceries, and the occasional night out, and it's no surprise so many students start wondering: Is there a way to make some extra money without wrecking my GPA? That's where side hustles come in. But the goal isn't just to find "something that makes money." A good side hustle for college students should fit around your schedule, skills, interests, academic responsibilities, and available resources, not force you to rearrange your entire life around it.
- [Why Didn’t They Teach Me This in School? Emotional Intelligence for Everyday Life](https://www.eliteacademicbrokers.com/emotional-intelligence-everyday-life/): These are the skills that make up what's commonly known as emotional intelligence, and while they rarely show up on a report card, they shape almost every important relationship and decision in our adult lives.
- [5 Nursing Care Plan Templates Every Student Should Have](https://www.eliteacademicbrokers.com/nursing-care-plan-templates-for-students/): That's exactly why having a set of reliable nursing care plan templates for students matters. Rather than rebuilding your care plan structure from scratch each time, you can identify the format you're asked for and adapt quickly.
- [What Is a Nursing Care Plan? A Beginner’s Guide](https://www.eliteacademicbrokers.com/what-is-a-nursing-care-plan/): So, what is a nursing care plan? In simple terms, it's a structured document that outlines a patient's nursing diagnoses, goals, and the interventions needed to reach those goals. It's built using the nursing process, often remembered by the acronym ADPIE, and it's one of the core skills every nursing student has to master.
- [Complete Guide to Nursing Rotation Plans and Their Importance](https://www.eliteacademicbrokers.com/nursing-rotation-plans/): While every program is structured somewhat differently, most nursing rotation plans include a recognizable set of core specialties. Understanding what each one is designed to teach helps students approach every placement with clearer expectations.
- [Best Nursing Student Planner Ideas for Academic Success](https://www.eliteacademicbrokers.com/best-nursing-student-planner-ideas/): In this article, you will learn what makes a planner genuinely useful for nursing school, the different planner formats available, the specific sections every nursing student planner should include, how to adapt a planner across BSN, MSN, and PhD programs, and practical tips for building a sustainable planning habit that lasts beyond a single semester. Whether you prefer a paper planner you can carry into clinical or a digital system synced across your devices, the goal is the same: less mental clutter and more confidence walking into every exam, skills check, and patient assignment.
- [What Nursing Professors Wish Every Student Knew](https://www.eliteacademicbrokers.com/what-nursing-professors-wish-every-student-knew/): Every semester, nursing professors watch bright, hardworking students struggle with the same invisible obstacles. These are not gaps in intelligence or effort. They are gaps in the unwritten rules of nursing school, the habits of thinking, and the professional instincts that textbooks rarely spell out directly. Faculty often say the same things privately in office hours or during clinical debriefs, yet these lessons rarely make it into a single organized resource for students.
- [Evidence-Based Practice in Nursing:  The Complete Student Guide (2026)](https://www.eliteacademicbrokers.com/evidence-based-practice-in-nursing/): Evidence-based practice in nursing is no longer optional. It is the gold standard of modern healthcare. Whether you are a first-year nursing student or a seasoned registered nurse, understanding how to use the best available evidence to guide patient care is one of the most important skills you can develop.
- [Reflective Nursing Essay Guide: How to Write an Outstanding Nursing Reflection Step-by-Step](https://www.eliteacademicbrokers.com/reflective-nursing-essay-guide/): If you have ever stared at a blank page wondering where to begin your nursing reflection, you are not alone. Reflective writing is one of the most valuable  yet most misunderstood  skills in nursing education. This reflective nursing essay guide breaks the entire process down into clear, practical steps so you can write with confidence from your very first sentence to your final conclusion.
- [APA 7 Citation Guide](https://www.eliteacademicbrokers.com/apa-7-citation-guide/): Every student has been there. You spend hours writing an excellent essay, then lose marks because a reference is formatted incorrectly or an in-text citation is missing. Mastering the APA 7 Citation Guide is one of the most powerful investments you can make in your academic career. This comprehensive guide will walk you through everything you need to know about APA 7th Edition referencing  from formatting your title page to citing AI tools correctly.
- [NCLEX Study Plan: The Ultimate 30-Day NCLEX Study Plan to Pass on Your First Attempt](https://www.eliteacademicbrokers.com/nclex-study-plan-30-days/): A complete, evidence-informed 30-day NCLEX study plan with a day-by-day schedule, daily routine, and proven study strategies for nursing students.
- [Nursing Student Life, Study Tips, Clinical Experience, Nursing School Schedule](https://www.eliteacademicbrokers.com/day-in-the-life-of-a-nursing-student/): The day in the life of a nursing student is not glamorous. It is early mornings, clinical uncertainty, pharmacology mnemonics, and the occasional moment of genuine wonder when a skill you practiced a hundred times in simulation finally clicks in a real clinical setting.
- [AI for Nursing Students: 12 Tools That Make Studying Easier](https://www.eliteacademicbrokers.com/ai-for-nursing-students-study-tools/): Used well, AI for nursing students is not about cutting corners. It is about reclaiming hours that used to disappear into rewriting notes, hunting for practice questions, or untangling a confusing pathophysiology concept at 11 p.m. the night before an exam. Used poorly, it can become a crutch that quietly erodes the clinical reasoning skills nursing programs are designed to build.
- [How to Remember Nursing Notes Without Forgetting](https://www.eliteacademicbrokers.com/how-to-remember-nursing-notes/): If you are a nursing student or a practicing nurse, you already know the challenge: pages upon pages of clinical notes, drug classifications, lab values, care plans, and medical terminologies that seem to evaporate the moment you walk out of the lecture hall or step away from the chart. The question of how to remember nursing notes is one of the most frequently searched topics among nursing students worldwide, and for good reason.
- [What to Do When You Feel Like Quitting Nursing School](https://www.eliteacademicbrokers.com/quitting-nursing-school/): You are sitting in the library at midnight, surrounded by pharmacology notes and you feel like quitting nursing school. Your clinical evaluation did not go the way you hoped. Your bank account is thinning. Your social life has all but disappeared. And somewhere between the third failed quiz attempt and the fifth pot of coffee, a thought surfaces that you have been trying to push away for weeks:
- [Nursing Student Burnout: Warning Signs and Proven Solutions](https://www.eliteacademicbrokers.com/nursing-student-burnout-signs-and-solutions/): Nursing school is one of the most demanding academic journeys a person can undertake. Between rigorous coursework, back-to-back clinical rotations, NCLEX preparation, and the emotional weight of patient care, it is no surprise that nursing student burnout has become a growing crisis in healthcare education.
- [Patient Assessment Form Nursing Template: A Complete Guide for Healthcare Professionals](https://www.eliteacademicbrokers.com/patient-assessment-form-nursing-template/): For nurses, documentation is not a bureaucratic after thought, it is a clinical tool as important as a stethoscope. A well-designed patient assessment form nursing template gives healthcare professionals a reliable framework to gather, organize, and act on patient information from the very first moment of contact. Whether you are working in a busy emergency department, a long-term care facility, or delivering home health services, having a structured assessment template is the foundation of safe, evidence-based nursing practice.
- [SBAR Template for Nursing Students](https://www.eliteacademicbrokers.com/sbar-template-for-nursing-students/): Check out Free SBAR_Template for Nursing students 
- [Common Nursing Diagnoses and Interventions List](https://www.eliteacademicbrokers.com/common-nursing-diagnoses-and-interventions-lists/): The common nursing diagnoses and interventions list is not just an academic exercise  it is a practical tool that shapes every nursing care plan. Here is why this matters in real clinical practice:
- [Basic Concepts Every Nursing Student Must Know](https://www.eliteacademicbrokers.com/basic-concepts-every-nursing-student-must-know/): This comprehensive guide walks you through the basic concepts every nursing student must know before stepping into a clinical setting. Whether you are just starting your program or looking to reinforce your foundation, this guide covers everything from anatomy to ethics, patient assessment to communication, and pharmacology to legal accountability.
- [5HR03 Reward for performance and contribution](https://www.eliteacademicbrokers.com/5hr03-reward-for-performance-and-contribution/): https://www.cipd.co.uk/knowledge/strategy/reward/strategic-total-factsheet
- [Nursing Student Burnout: 12 Warning Signs You Can’t Ignore (And How to Recover)](https://www.eliteacademicbrokers.com/nursing-student-burnout-signs-solutions/): If that sounds familiar, you may be experiencing nursing student burnout  a condition that affects an estimated 40–50% of nursing students worldwide, yet remains dangerously under-discussed in academic settings.
- [How to Deal With Stress in Nursing School: 12 Proven Strategies](https://www.eliteacademicbrokers.com/stress-in-nursing-school/): Nursing school is one of the most demanding academic journeys you can take. Between rigorous coursework, clinical rotations, and the weight of learning to care for real patients, stress in nursing school is practically a rite of passage  but it doesn't have to derail you.
- [Nursing Care Plan Template for Students: A Complete Step-by-Step Guide](https://www.eliteacademicbrokers.com/nursing-care-plan-template/): Writing a nursing care plan can feel overwhelming for many student nurses, especially during clinical rotations and exams. A well-structured nursing care plan template for students helps simplify the process by organizing patient assessment, nursing diagnoses, goals, interventions, and evaluation in a clear format. You will learn how to create effective nursing care plans, avoid common mistakes, and use practical examples to improve your clinical documentation skills and patient care.
- [How to Write a PICOT Question in Nursing (With Examples)](https://www.eliteacademicbrokers.com/picot-questions-in-nursing/): 💡  Whether you're a first-year nursing student or preparing your capstone project, mastering the PICOT questions in nursing  format is one of the most valuable skills you can build. This guide breaks it down step by step  with a free template and real examples you can use today.
- [NCLEX Practice Questions With Rationales PDF: The Complete Study Guide](https://www.eliteacademicbrokers.com/nclex-practice-questions/): NCLEX practice questions with rationales are the single most powerful tool in your exam preparation arsenal. Rationales explain not just why the correct answer is right, but why every other option is wrong. That distinction is the foundation of the clinical reasoning the NCLEX is explicitly designed to test. This guide covers how to use practice questions with rationales strategically, where to find the best free and paid PDF resources, and how to make every question count.
- [The Ultimate Nursing Exam Revision Checklist: Everything You Need to Study and Pass](https://www.eliteacademicbrokers.com/nursing-exam-revision-checklist/): Exam season in nursing school is one of the most high-stakes periods of your academic life. The content is vast, the stakes are real, and the margin for under-preparation is thin. Many nursing students struggle not because they lack intelligence or dedication, but because they lack a clear, structured system for revision. That is exactly what a nursing exam revision checklist provides.
- [Drugs every nursing student must know](https://www.eliteacademicbrokers.com/drugs-every-nursing-student-must-know/): Pharmacology is one of the most challenging  and most critical  subjects a nursing student will ever master. With hundreds of medications in clinical circulation, knowing which drugs to prioritize can feel overwhelming. That is why we have compiled this comprehensive guide to the top 100 drugs every nursing student must know  the medications most likely to appear on the NCLEX-RN, NCLEX-PN, and in everyday clinical practice.
- [ECG Interpretation Explained Step by Step for Nurses](https://www.eliteacademicbrokers.com/ecg-interpretation-step-by-step-nursing/): This guide walks you through ECG interpretation step by step  from understanding the basics of cardiac electricity to identifying key waveforms and rhythms in clear, nurse-friendly language.
- [How Many Hours Should a Nursing Student Study Per Day? The Honest Answer](https://www.eliteacademicbrokers.com/how-many-hours-should-a-nursing-student-study-per-day/): Ask any nursing student about their biggest challenge and most will not say the exams  they will say managing the time needed to prepare for them. Between lectures, clinical rotations, care plans, and personal responsibilities, one question comes up constantly: how many hours should a nursing student study per day?
- [How to Take Effective Notes in Nursing School: A Complete Guide for Students](https://www.eliteacademicbrokers.com/how-to-take-effective-notes-in-nursing-school/): Nursing school is one of the most demanding academic journeys a student can undertake. Between anatomy lectures, pharmacology modules, and clinical rotations, the sheer volume of information can feel overwhelming. One skill that separates students who thrive from those who merely survive is knowing how to take effective notes in nursing school.
- [Common Nursing Diagnoses and Interventions List: A Complete Clinical Reference](https://www.eliteacademicbrokers.com/common-nursing-diagnoses-and-interventions-list/): Every nurse, from a first-year student to a seasoned practitioner, relies on one essential clinical tool: the nursing diagnosis. Understanding the most common nursing diagnoses and interventions is not just an academic exercise, it is the foundation of safe, structured, and patient-centred care.
- [Nursing Care Plan Examples for Beginners: A Complete Step-by-Step Guide](https://www.eliteacademicbrokers.com/nursing-care-plan-examples-for-beginners/): This guide breaks down nursing care plan examples for beginners in a clear, practical, and actionable way. You'll learn the five-step nursing process, understand NANDA-I nursing diagnoses, and walk through real care plan templates you can adapt for your patients today.
- [Top 10 NCLEX Practice Question Tips to Pass Your Exam](https://www.eliteacademicbrokers.com/nclex-practice-question-tips/): If you are preparing for the NCLEX, you already know that practice questions are the backbone of effective exam prep. But not all practice is created equal. Simply answering hundreds of NCLEX practice questions without a strategy can leave you feeling overwhelmed and underprepared.
- [How to Improve Nursing Grades Fast: 8 Proven Strategies That Work](https://www.eliteacademicbrokers.com/improve-nursing-grades-fast/): Struggling to keep your nursing grades where they need to be? You’re not alone. Nursing school is widely known as one of the most demanding academic paths, combining intense coursework, clinical rotations, and high-stakes exams that test both knowledge and critical thinking.
- [How to Pass Nursing Exams Even If You’re Struggling](https://www.eliteacademicbrokers.com/how-to-pass-nursing-exams/): This guide walks you through everything you need to know about how to pass nursing exams, from building a smart study plan to mastering test-taking techniques that actually work.
- [ABG Practice Questions With Answers (Step-by-Step Solutions)](https://www.eliteacademicbrokers.com/abg-practice-questions-nursing/): In this post, you will work through 10 ABG practice questions nursing students encounter most often, complete with step-by-step solutions so you can see exactly how to arrive at the correct answer, not just memorize it.
- [Iowa Model of Evidence-Based Practice Explained: A Complete Guide for Nurses](https://www.eliteacademicbrokers.com/iowa-model-of-evidence-based-practice/): The Iowa Model of Evidence-Based Practice (EBP) was developed to answer exactly that question. It gives nurses and healthcare teams a structured, step-by-step framework to translate research into real-world clinical action. Whether you are a nursing student encountering EBP for the first time or a seasoned clinician leading a practice change initiative, understanding the Iowa Model is essential.
- [How to Write a Nursing Literature Review: A Complete Step-by-Step Guide](https://www.eliteacademicbrokers.com/how-to-write-a-nursing-literature-review/): Knowing how to write a nursing literature review is not simply an academic requirement. It is a clinical skill. It trains you to evaluate evidence critically, recognise gaps in current practice, and apply research findings meaningfully to patient care.
- [How to Write a Nursing Assignment Introduction](https://www.eliteacademicbrokers.com/nursing-literature-review/): This explains exactly how to write a nursing assignment introduction, covering structure, content, clinical context, and common mistakes to avoid. Whether you are writing a reflective essay, a care plan analysis, or a research-based assignment, these principles apply.
- [How to Formulate PICOT Questions: A Complete Nursing Guide](https://www.eliteacademicbrokers.com/how-to-formulate-picot-questions-nursing/): Knowing how to formulate PICOT questions is a foundational skill in nursing education and evidence-based practice (EBP). Whether you are completing a nursing assignment, conducting a literature review, or driving quality improvement on your unit, a well-constructed PICOT question directs your research with precision and purpose.
- [Steps of Evidence-Based Practice in Nursing (EBP Guide)](https://www.eliteacademicbrokers.com/steps-evidence-based-practice-nursing/): This will breaks down the core steps of evidence-based practice in nursing, provides clinical examples, and offers practical tools to apply EBP in both academic assignments and real-world healthcare settings.
- [Top 50 Nursing Mnemonics You Must Know](https://www.eliteacademicbrokers.com/nursing-mnemonics/): Whether you're studying for the NCLEX-RN, preparing for a clinical shift, or brushing up on core concepts, this guide covers the top 50 nursing mnemonics every nurse must know  organized by topic for fast reference.
- [Maslow’s Hierarchy of Needs in Nursing Practice](https://www.eliteacademicbrokers.com/maslows-hierarchy-of-needs-in-nursing-practice/): This is exactly where Maslow's hierarchy of needs in nursing becomes indispensable. Originally developed by psychologist Abraham Maslow in 1943, this framework has become one of the most powerful tools in nursing practice. It gives nurses a structured, human-centered way to prioritize care, build therapeutic relationships, and deliver holistic treatment.

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- [FAQ](https://www.eliteacademicbrokers.com/faq/frequency-asked-questions/): Our services encompass a wide range of academic needs including but not limited to essay writing, research paper assistance, editing and proofreading, thesis and dissertation support, homework help, and tutoring.

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In doing so, this will delete the previous version which you submitted and your new updated version will replace it. Therefore your Turnitin similarity score should not be affected. If there is a change in your Turnitin similarity score, it will be due to any changes you may have made to your Coursework. • If, for whatever reason, you have issues uploading your assignment to the dedicated submission link on the VLE, you must immediately log an enquiry with University of London through your Student Portal and attach your assignment to that enquiry. • Please note, when the due date is reached, the version you have submitted last, will be considered as your final submission and it will be the version that is marked. • Once the due date has passed, it will not be possible for you to upload a different version of your assessment. Therefore, you must ensure you have submitted the correct version of your assessment which you wish to be marked, by the due date. 1 | P a g e Coursework Brief: The Research Project 2: Consolidation module is assessed entirely through coursework (there is no exam). The Research Project (or Research Proposal) counts for 100% of your grade and must follow the structured format provided. Templates and guidance notes are available in the Assessment section of the VLE. Producing your final year research project is a central requirement of your psychology degree. This assignment allows you to demonstrate the knowledge and skills you have acquired throughout your studies and to showcase how you have applied them to a real world research problem. You will develop critical thinking, research design, and data analysis skills, as well as a clear understanding of the ethical considerations involved in research. This prepares you for future academic or professional work as an independent researcher. The report must follow current APA style. Tables and figures should be included within the main body of the text at the appropriate points, not at the end of the report. Report Structure The report is made up of the following sections. The headings and subheadings listed must be included. Some suggested subsections are also provided (shown in italics). Title Page Include: • Student ID number (not your name) • Full project title • Module title and code • Word count • Statement of contribution Statement of Contribution Clearly state which work you carried out (e.g., hypothesis formation, recruitment, data collection, analyses, interpretation). Indicate whether each element was completed independently or jointly with supervisors or other researchers. Abstract • For quantitative projects: use a structured abstract with the headings Background, Aims, Method, Results, Conclusion. • For qualitative projects: you may omit any headings that are not relevant. Although APA style does not normally include headings in abstracts, you must include them here. Introduction A strong introduction engages the reader with the research problem and sets the context for the study. It should establish why the topic is important, situate the study in relation to current knowledge, and highlight prior theoretical and empirical work. It is not necessary to 2 | P a g e review every study, but the most relevant and recent literature should be included, with proper credit to other researchers. The introduction should conclude with a clear statement of the overarching research question. Depending on your design, you may also include research aims, hypotheses, or propositions. If you present more than one hypothesis or proposition, number them clearly. Method Describe your study in sufficient detail for replication (i.e., so another researcher could reproduce it exactly). This section will vary depending on your study. Possible subsections include (depending on your design): Design Provide a concise overview of your study type (e.g. experimental, survey, qualitative, or secondary analysis Participants Describe sampling and recruitment methods, inclusion or exclusion criteria, sample size, and dropouts (those excluded after data collection and why). Participant characteristics (e.g., age, gender) should be reported in the Results, not here. Materials or Measures Describe what was used in the study. For questionnaires, include the instrument name, its main features, response type, example items, scoring method (e.g., mean or sum scores), possible range, and reliability evidence if available. Procedure Describe exactly what happened in the study. Include consent, randomisation or matching, the tasks participants completed, how data were collected, and any debriefing procedures. For qualitative projects, you must explain how recordings were pseudonymised and anonymised during transcription, coding, and analysis. Statistical Analysis Most projects will contain a short explanation of the statistical analysis techniques used in the study. This should clarify the statistical techniques used and justify the choice of methods, demonstrating the rigour of the analysis, and providing a framework for interpreting the results. • For quantitative projects, you should also summarise what data cleaning, if any, was undertaken and how much (%) data was lost as a result (i.e., ‘missing data’). • For qualitative projects, you should also describe how data were collected and transcribed, and the type of analysis framework that was used. Results Do not include raw, unsummarised data or any identifying material. Structure your Results according to the conventions of your study design. 3 | P a g e Sections may include: • Participant Characteristics: number, age, gender, etc. Include a table if appropriate. Test for group differences where relevant. • Summary of Main Data: e.g., means, standard deviations, correlations, reliability. • Inferential Analyses: directly test your hypotheses. Use hypotheses as subheadings if helpful. Avoid including irrelevant analyses. • Qualitative Analyses: describe data organisation, present themes, provide supporting quotations. Tables and Figures Use tables and figures (i.e. charts, graphs and pictures) to display the most important results from your main analyses. • Maximum of 5 in the Results section. • Number consecutively and cite in-text. • Each must stand alone with a clear take-home message. Discussion Must include: • A clear statement of support or non-support for each hypothesis. • Explanations for findings (including null results). • Critical interpretation of results, considering: o Bias, validity threats, measurement issues o Adequacy of sample and statistical power o Overlap among tests or multiple comparisons o Note: These critical reflections are suggestions rather than a comprehensive or mandatory list. Strengths and Limitations • For quantitative projects, consider issues of generalisability, ecological validity, and sampling validity, noting any challenges (e.g., missing data, dropouts) and how these were managed. • For qualitative projects, consider transferability rather than generalisability, reflect on ecological validity (authenticity of context and responses), and address sampling limitations. Note challenges such as recruitment or achieving data saturation and how these were overcome. • Note: These strengths and limitations are suggestions rather than a comprehensive or mandatory list. Implications • Reflect on conceptual, methodological, and practical significance. • Suggest directions for future research, policy and/or practice where relevant. Conclusion • Summarise the overall conclusions (broader than results). • Relate clearly back to the title and research question. • Highlight key next steps or implications. Note: If you find material that does not fit into these sections, it is unlikely to be relevant and should be removed. 4 | P a g e References Follow APA style. No maximum, but 20–40 is recommended. Appendices Include material that is too detailed for the main body. Mandatory appendices: • A link to your UoL-provided OSF section, which must: 1. Be private (not public) 2. Be set to Germany-Frankfurt storage 3. Contain three components: Data, Data analysis plan, Participant information 4. Be the OSF section set up for you by UoL (not one you created yourself) 5. Contain all specified UOL contributors (as explained in the module information on the VLE) Optional content (where relevant): Otherwise, it is your decision to determine which information to include in the main body of your report, OSF, or appendices. Consider the most effective and efficient way to present your findings to your reader. • Raw qualitative data • Extra tables • Questionnaires or other research instruments • Stimuli or materials used • Extracts from interview transcripts Assessment Criteria: Please refer to Appendix D of the Programme Regulations for detailed Assessment Criteria. AND Please ensure that you also refer to the specific marking criteria for this module, as these are an important supplement to the general marking criteria. The specific marking criteria can be found on the main page of the Assessment section. Plagiarism: This is cheating. Do not be tempted and certainly do not succumb to temptation. Plagiarised copies are invariably rooted out and severe penalties apply. All assignment submissions are electronically tested for plagiarism. More information may be accessed via: Assessment offences and cheating | University of London 5 | P a g e Artificial Intelligence (AI): For BSc Psychology Programme specific guidance on the permitted usage of AI as a supportive tool, please refer to the coursework coversheet, which can be located alongside this assessment brief on your module VLE assessment area. In addition, the following guidance is provided in sections 7.1 & 7.9 of the University of London General Regulations 2025-26: 7.1 All work which you submit for assessment must be your own, expressed in your own words and include your own ideas and judgements. By submitting work for assessment you confirm that the work is entirely your own, that you have acknowledged the work of other people within your submission, in line with our requirements, and that you understand what is meant by plagiarism, self-plagiarism, collusion, contract cheating and research misconduct. 7.9 Except in cases where their use is explicitly required or permitted for a particular assessment, submitting work which has been generated by software, or derived from prompts or queries provided to any third-party service, including use of Large Language Model/Generative AI/AI chatbots, either in full or part, is an Assessment offence. Where usage is permitted for an assessment, the use of these tools should be appropriately acknowledged. Coursework Coversheet: A coursework coversheet can be located alongside this coursework brief in the assessment area of your module VLE. Please ensure that you complete the fields for ‘student number’ and ‘word count’on the first page, and the table on second page with check boxes and free type fields in relation to the declaration of AI usage. Please ensure that you attach the COMPLETED coversheet to your submitted work. Failure to submit a completed coversheet with your work will result in a 5 mark deduction. Penalties for exceeding the word count: What counts towards the word count • Included: the main body of text, in-text citations, references within the text, quotations, headings, and subheadings. • Not included: cover page, title, abstract, tables and figures (and their captions), reference list, and appendices. • Footnotes are not allowed. Limits for different sections • Title: maximum of 20 words. 6 | P a g e • Abstract: maximum of 250 words. • Appendices: maximum of 2,000 words. • Tables and figures: up to five in total (in any combination of tables/figures). 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2.1.5 Time-FrequencyAnalysisviaContinuousWaveletTransform. . . . 13 2.2 ExploratoryDataAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.1 MarketversusStockBetas&CAPMrisk. . . . . . . . . . . . . . . 15 2.2.2 Market-level trenddrawdown&Regimeclassification . . . . . . . . 15 2.2.3 Vol-regimeZ-scores&Volatilitytermstructure . . . . . . . . . . . 16 2.2.4 MeanReversion&TrendConsistency. . . . . . . . . . . . . . . . . 18 2.2.5 Stock-LevelTrendOscillatorsandBoundedPercentileMetrics . . . 20 2.2.6 RSIvs.Pricevs.StochasticMomentum. . . . . . . . . . . . . . . . 21 2.2.7 StockMarketStructureandVolatilityCompression . . . . . . . . . 23 2.2.8 Stock-LevelTrendStrengthandReliability . . . . . . . . . . . . . . 25 2.2.9 RiskRegimeAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 TimeSeriesDecompositionAnalysis . . . . . . . . . . . . . . . . . . . . . 29 2.3.1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 StatisticalHypothesisTestingandInference 34 3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 SOICT-HUST StockPriceAnalysis 2 3.1.1 Group1:TimeSeriesCharacteristics . . . . . . . . . . . . . . . . . 34 3.1.2 Group2:TechnicalAnalysisandMicrostructure . . . . . . . . . . . 35 3.1.3 Group3:MarketIndexRelationships . . . . . . . . . . . . . . . . . 35 3.2 HypothesisTestingResults . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.1 Group1:TimeSeriesCharacteristicsofFPT. . . . . . . . . . . . . 36 3.2.2 Group2:TechnicalAnalysisandMicrostructureSignals. . . . . . . 37 3.2.3 Group3:MarketIndexRelationships . . . . . . . . . . . . . . . . . 38 3.3 ConclusionandModelingImplications . . . . . . . . . . . . . . . . . . . . 38 3.3.1 SummaryofStatisticalFindings . . . . . . . . . . . . . . . . . . . . 38 3.3.2 ImplicationsforFeatureSelection . . . . . . . . . . . . . . . . . . . 39 3.3.3 ImplicationsforForecastingModels . . . . . . . . . . . . . . . . . . 39 4 ForecastingModelDevelopment 40 4.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2 DataRepresentationandFeatureEngineering . . . . . . . . . . . . . . . . 41 4.2.1 MarketFeatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2.2 StockFeatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2.3 DataProcessing&Pipeline . . . . . . . . . . . . . . . . . . . . . . 44 4.3 ModelSelection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3.1 SummaryofSelectedFeatures . . . . . . . . . . . . . . . . . . . . . 48 4.3.2 ClassicalModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3.3 MachineLearningModels . . . . . . . . . . . . . . . . . . . . . . . 49 4.3.4 DeepLearningModels . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.4 HyperparameterOptimization . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.4.1 OptimizationMethodology. . . . . . . . . . . . . . . . . . . . . . . 51 4.4.2 HyperparameterSearchSpaces . . . . . . . . . . . . . . . . . . . . 51 4.4.3 SummaryofSearchSpaceParameters. . . . . . . . . . . . . . . . . 52 5 ModelEvaluationandConclusion 54 5.1 ForecastingPerformanceEvaluation. . . . . . . . . . . . . . . . . . . . . . 54 5.1.1 ExperimentalSetup. . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.1.2 EvaluationMetrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.1.3 ForecastingResults . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.2 StatisticalReliabilityofForecasts . . . . . . . . . . . . . . . . . . . . . . . 56 5.2.1 BootstrapConfidenceIntervals . . . . . . . . . . . . . . . . . . . . 56 5.2.2 Diebold–MarianoTest . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.3 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.4 FutureWork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 SOICT-HUST Stock Price Analysis 3 Chapter 1 Introduction 1.1 Abstract Stock price forecasting is challenging because financial time series are noisy, non stationary, heavy-tailed, and affected by time-varying volatility. This study analyzes and forecasts Vietnamese stock market data, focusing on FPT as the main stock and using VNINDEX and VN30 as market references. The goal is not to guarantee profitable trad ing decisions, but to build a statistically grounded framework for understanding market behavior and comparing forecasting models. The dataset is collected from VNStock and includes daily OHLCV data for FPT, VNINDEX, and VN30. From the raw data, we construct log returns, lagged returns, rolling statistics, volume-based features, technical indicators, and market-related vari ables. We first conduct exploratory data analysis and statistical hypothesis tests, includ ing stationarity, normality, autocorrelation, volatility clustering, Granger causality, vari ance comparison, and market beta analysis. Then, we compare classical models such as ARIMA/SARIMAX and GARCH-type models with machine learning models, including XGBoost, MLP, LSTM, and GRU. The empirical results show that FPT closing prices are non-stationary, while log re turns are stationary. FPT returns also exhibit heavy tails and strong volatility clustering, suggesting the need for robust metrics and volatility-aware features. In addition, FPT has significant exposure to VNINDEX, showing that market-level movement is important for explaining individual stock behavior. Model performance is evaluated using MAE, RMSE, MAPE, directional accuracy, Diebold–Mariano tests, bootstrap confidence intervals, and multi-horizon forecasting. SOICT-HUST Stock Price Analysis 4 1.2 Related Works 1.2.1 Classical Statistical Approaches Classical time-series models such as ARIMA are widely used as interpretable base lines for forecasting. The Box–Jenkins framework provides a systematic way to model autoregressive and moving-average structures in stationary or differenced time series . Since raw stock prices are often non-stationary, unit-root testing is necessary before model fitting. The Dickey–Fuller test provides a standard method for detecting unit roots and deciding whether differencing is required . Financial returns also commonly exhibit volatility clustering, where large price changes tend to be followed by large changes. Engle introduced the ARCH model to capture conditional heteroskedasticity , and Bollerslev extended it into the GARCH model by including past conditional variances . These models are important because stock-market risk is often time-varying rather than constant. Market relationship analysis is another important part of financial modeling. The Effi cient Market Hypothesis suggests that historical prices alone may have limited predictive power in efficient markets . Meanwhile, the Capital Asset Pricing Model measures sys tematic market exposure through beta . In this project, these ideas motivate the use of VNINDEX and VN30 as market-level references when analyzing FPT. 1.2.2 Machine Learning in Finance Machine learning models are often used in financial forecasting because they can cap ture nonlinear relationships among features. XGBoost is a scalable gradient boosting method that performs well on structured tabular data and can model complex feature interactions . Therefore, it is suitable for combining OHLCV variables, technical indi cators, volume features, and market-index returns. Deep learning models are also useful for sequential data. LSTM networks were designed to learn long-term dependencies and reduce the vanishing-gradient problem in recurrent neural networks . GRU is a simpler gated recurrent architecture that can also capture temporal dependencies with fewer parameters . In this study, LSTM and GRU are used to test whether recurrent models can improve short-horizon stock forecasting. However, complex models can easily overfit noisy financial data. Therefore, model comparison should not rely only on one error metric. The Diebold–Mariano test provides a formal way to test whether two forecasting models have significantly different predictive accuracy . This project therefore evaluates models using both standard metrics and statistical comparison tests. SOICT-HUST Stock Price Analysis 5 1.2.3 Research Gap Many studies focus either on statistical testing or on predictive modeling. Pure statis tical approaches are interpretable but may miss nonlinear patterns, while pure machine learning approaches may ignore important properties such as non-stationarity, heavy tails, and heteroskedasticity. This project bridges that gap by combining hypothesis testing, sig nal processing, and predictive modeling in one workflow. Statistical tests guide feature construction and model selection, while machine learning models are used to evaluate predictive performance. 1.3 Research Objectives The core objectives of this study are threefold: • Statistical Testing: To identify key statistical properties of FPT, VNINDEX, and VN30, including non-stationarity, heavy-tailed returns, autocorrelation, volatility clustering, volume-related risk, and market dependence. • Feature Engineering: To transform raw OHLCV data into useful predictive fea tures, including log returns, lagged returns, rolling statistics, technical indicators, market variables, and decomposition-based components. • ModelConstruction and Evaluation:TobuildandcompareARIMA/SARIMAX, GARCH-typemodels,XGBoost,MLP,LSTM,andGRUusingMAE,RMSE,MAPE, directional accuracy, Diebold–Mariano tests, bootstrap confidence intervals, and multi-horizon forecasting. This study aims to answer the following questions: 1. Are FPT prices and log returns stationary? 2. Do FPT returns exhibit heavy tails or volatility clustering? 3. Do volume, technical indicators, VNINDEX, and VN30 provide useful predictive information? 4. Do machine learning and deep learning models outperform classical statistical base lines? 5. Which feature groups contribute most to forecasting performance? SOICT-HUST Stock Price Analysis 6 Chapter 2 Signal and Exploratory Data Analysis 2.1 Signal Statistics 2.1.1 Log-return as a High-Pass Filter In financial time-series analysis, the continuous compounding return, or log-return, is defined as: rt = log Pt Pt−1 = log(Pt)−log(Pt−1) (2.1) where Pt is the asset price at time t. By defining the log-price as pt = log(Pt), the log return can be expressed simply as the first difference of the log-price series: rt = pt−pt−1. From a signal processing perspective, this differencing operation acts as a linear time invariant (LTI) filter applied to the log-price signal. Let the impulse response of this filter be h. The output rt is the convolution of pt with h, where h = 1, h = −1, and h = 0 otherwise. Taking the discrete-time Fourier transform (DTFT) of the impulse response yields the frequency response function H(eiω): ∞ H(eiω) = n=−∞ he−iωn = 1 −e−iω (2.2) where ω ∈ represents the angular frequency. Therefore, we calculate its squared magnitude: |H(eiω)|2 = (1 − e−iω)(1 − eiω) = 2(1 −cosω) (2.3) Analyzing this magnitude response reveals the filter’s characteristics across different frequencies: • Low Frequencies (ω → 0): As the frequency approaches zero, cos(ω) → 1, which means |H(eiω)|2 → 0. Low frequencies represent slow-moving, long-term macroe conomic trends in the stock price. The filter heavily attenuates these components, SOICT-HUST Stock Price Analysis 7 effectively removing the non-stationary "drift" or random walk component of the price series. • High Frequencies (ω → π): As the frequency approaches the Nyquist limit (π), cos(ω) → −1, which means |H(eiω)|2 → 4. High frequencies represent rapid, day to-day fluctuations and market microstructure noise. The filter not only retains but amplifies these high-frequency components. Therefore, transforming raw prices into log-returns systematically strips away the long term trend (low frequencies) while preserving the short-term volatility (high frequencies). Figure 2.1: Raw stock visualization Figure 2.2: Log-return transformation 2.1.2 Spectral and Autocorrelation Analysis To thoroughly understand the cyclical behavior and temporal dependencies of the financial time series, we utilize both frequency-domain and time-domain analytical tech niques. SOICT-HUST Stock Price Analysis 8 Power Spectral Density (PSD) In the frequency domain, the Power Spectral Density describes how the variance (or power) of a time series is distributed across different frequency components. To estimate the PSD of the log-returns robustly, we apply Welch’s method . Unlike a standard periodogram, which can be highly noisy, Welch’s method divides the time series into over lapping segments, computes a modified periodogram for each segment, and then averages these estimates. This averaging significantly reduces the variance of the power spectrum estimate. Given a sampling frequency of fs = 1 sample per trading day, the frequency f repre sents cycles per day. The reciprocal of the frequency yields the period T in days (T = 1/f). In financial markets, distinct periodicities often emerge due to trading schedules and macroeconomic reporting cycles. By plotting the PSD on a logarithmic scale, we can identify these latent seasonalities. For instance, a peak at f ≈ 0.20 corresponds to a 5-day cycle (weekly trading patterns), while a peak at f ≈ 0.047 corresponds to a 21-day cycle (typical number of trading days in a month). We utilize a segment length of 252 days to capture a full trading year of low-frequency dynamics. Autocorrelation and Partial Autocorrelation While the PSD identifies cyclical frequencies, the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) are time-domain tools essential for identifying the structural memory of the series. The ACF measures the linear dependence between the current value of the series, rt, and its past value at lag k, rt−k. It is defined as: ρk = Cov(rt,rt−k) Var(rt) (2.4) The ACF plot displays ρk against the lag k. The PACF, on the other hand, isolates the direct correlation between rt and rt−k by removing the linear influence of the intermediate lags (rt−1,rt−2,...,rt−k+1). Mathematically, it is the coefficient ϕkk in the autoregression of rt on its k past values. If the PACF cuts off abruptly after lag p while the ACF decays gradually, it indicates an AR(p) signature. 2.1.3 Ergodicity Checking A fundamental assumption in time-series forecasting is ergodicity, which implies that the time average of a single realization converges to the ensemble average (the expected value across all possible realizations) as the sample size grows. To empirically verify ergod icity, we must approximate an ensemble from a single observed realization. In this study, SOICT-HUST Stock Price Analysis 9 Figure 2.3: Auto and Partial-Auto Corre lation plot for log-returns of VNINDEX Figure 2.4: Power Spectral Density in fre quency domain we utilize two distinct simulation approaches: the K-Blocks method and the Stationary Bootstrap method. Method 1: The K-Blocks Approach The K-blocks method partitions the single observed time series into contiguous seg ments to simulate parallel universes. Let the time series of log-returns be denoted as {r1, r2, ...,rN}. We truncate the series slightly to length N′ such that it is perfectly divisible by a chosen integer K, resulting in a block size of M = N′/K. We construct an ensemble matrix where each row k represents a pseudo-independent realization (block), and each column t represents an intra-block time step:  r1   R=    rM+1 . . . r2 rM+2 . . . . . . rM . . . r2M . . . . . . r(K−1)M+1 r(K−1)M+2 ... rKM At each step t ∈ , the ensemble mean µ(E) t       and ensemble variance σ2(E) (2.5) are calculated down the columns across the K blocks. If the process is ergodic, these ensemble metrics should stabilize and closely track the expanding time-average metrics of the original series. t Method 2: Stationary Bootstrap Approach Financial returns often exhibit local dependencies (such as volatility clustering) that are destroyed by simple random sampling. To address this, we apply the Stationary Boot strap . Unlike a standard block bootstrap that uses fixed-length blocks, the stationary bootstrap resamples blocks of random lengths drawn from a geometric distribution with expected length λ. This randomization ensures that the resulting synthetic paths remain strictly stationary. We generate B synthetic time-series paths, each of length N, to form a robust ensemble. SOICT-HUST Stock Price Analysis 10 Let ˜rb,t represent the return at time t for the b-th bootstrapped path. The bootstrapped ensemble mean and variance at each time step t are given by: B µ(B) t = 1 B B b=1 ˜rb,t, σ2(B) t = 1 B−1 b=1 2 ˜ rb,t − µ(B) t (2.6) Because this method preserves the full temporal length N rather than truncating into sub-blocks, it provides a macro-level view of convergence. Evaluation of Ergodicity We visually compare the ensemble averages against the expanding time averages. The global mean µ and global variance σ2 serve as the asymptotic baselines. It can be observed (figure 2.5) that while the process is approximately ergodic w.r.t the mean (first moment), the variance depends on time step (heteroskedasticity), constrasting the homoskedasticity assumption of classic regression models. Figure 2.5: Time-averaged mean & variance versus. ensemble statistics 2.1.4 Karhunen-Loève and Empirical Mode Decomposition To isolate meaningful structural patterns from random market fluctuations, we con duct advanced signal decomposition techniques including Karhunen-Loève (K-L) Expan sion to analyze the variance structure across fixed time windows and Empirical Mode SOICT-HUST Stock Price Analysis 11 Decomposition (EMD), adaptively separating frequency components across the entire se ries. Karhunen-Loève Expansion and Volatility Clustering The Karhunen-Loève Expansion is a continuous analogue to Principal Component Analysis (PCA). It projects a stochastic process onto a set of orthogonal basis func tions, or eigenfunctions, ordered by the amount of variance they explain. When applied to rolling 20-day windows (representing a standard trading month), the K-L expansion reveals distinct differences in the predictability of directional returns versus market risk. As shown in the cumulative explained variance analysis, raw returns exhibit behavior consistent with the Efficient Market Hypothesis (EMH). The variance explained by the principal components of raw returns grows linearly, indicating a highly noisy process dom inated by idiosyncratic shocks where no small set of components can adequately capture the total variance. Meanwhile, the squared returns—acting as a proxy for volatility— demonstrate pronounced volatility clustering. The first few components capture a signif icantly larger share of the variance (crossing the 50% threshold by the 6th component), confirming that market risk contains a strong, low-dimensional underlying structure. The first few eigenfunctions exhibit shapes that resemble well-known signal-processing filters: • PC1: A smooth, predominantly positive loading across the entire window, acting as a low-frequency mode that captures the overall level of returns or volatility. • PC2: A single sign change within the window, contrasting observations from the first and second halves of the month and representing an intermediate-frequency mode. • PC3: Multiple sign changes and oscillatory behavior, corresponding to higher frequency fluctuations within the window. The eigenfunctions for volatility are notably smoother than those of raw returns, further emphasizing that market volatility concentrates in clusters and evolves more predictably than market direction. Empirical Mode Decomposition (EMD) While the K-L expansion is constrained by a fixed window size, Empirical Mode De composition (EMD) is a fully data-driven approach that assumes no a priori basis func tions . EMD utilizes a sifting process to decompose the non-linear and non-stationary log-return series into a finite set of Intrinsic Mode Functions (IMFs). Each IMF represents a simple oscillatory mode with a distinct, locally defined frequency. SOICT-HUST Stock Price Analysis 12 In our experiment, the EMD applied to log-returns yields 16 distinct IMFs, effectively separating the market’s temporal dynamics: • High-Frequency Modes (IMF 1–4): These components contain the highest frequencies and lowest amplitudes. They primarily capture market microstructure noise, daily bid-ask bounce, and rapid, transient shocks. • Intermediate Cycles (IMF 5–12): These modes represent medium-term market memory, capturing weekly, monthly, and quarterly trading cycles, as well as the momentum effects driven by institutional rebalancing and earnings reports. • Low-Frequency Trends (IMF 13–16): The final IMFs and the residual represent the slow-moving macroeconomic drift. They reflect long-term structural changes in the Vietnamese economy and broad market cycles spanning multiple years. Figure 2.6: K-L expansion of Raw log-return signal Figure 2.7: Some IMF modes decomposed SOICT-HUST Stock Price Analysis 13 2.1.5 Time-Frequency Analysis via Continuous Wavelet Trans form To capture localized time-frequency dynamics, we apply the Continuous Wavelet Transform (CWT). Unlike the Fourier transform, which uses infinite sine waves, CWT uses localized "wavelets" that expand and contract to measure both when and at what frequency structural shifts occur . Using the Morlet wavelet as the mother wavelet, the CWT of the log-return series rt at scale a and translation (time) b is defined as the convolution: W(a,b) = 1 √ a ∞ −∞ rtψ∗ t−b a dt where ψ∗ is the complex conjugate of the Morlet wavelet function. The scale a is inversely proportional to frequency: low scales correspond to high-frequency, short-term market noise, while high scales correspond to low-frequency, long-term macroeconomic trends. The localized variance, or wavelet power, is calculated as the squared magnitude of the coefficients: P(a,b) = |W(a,b)|2 . Interpretation of the Scalogram The CWT Scalogram visualizes the wavelet power across time and scales, with some insights regarding the return dynamics: • Volatility Cascades: The bright regions (pink/light orange) representing high wavelet power do not occur as horizontal bands (which would imply a constant cy cle). Instead, they manifest as vertical "cones" or pillars. This indicates that major market shocks are localized in time and cascade across multiple scales simultane ously, disrupting both short-term trading patterns and long-term momentum. • Short-Term Dominance during Crises: The highest power concentrations con sistently appear at the top of the y-axis (scales a < 50). This confirms that during periods of extreme market turbulence, a larger fraction of the local variance is con centrated in short-term fluctuations. Dominant Time Scale Dynamics To further quantify these shifts, we extract the dominant time scale at each time step t, defined as the scale that maximizes the wavelet power: a∗ t = arg max a P(a,t) The dominant scale frequently oscillates between two extremes: SOICT-HUST Stock Price Analysis 14 • High-Scale Regimes (a ≈ 150−250): During relatively calm market periods (e.g: 2018-2019), variance is primarily associated with slower-moving market dynamics and persistent trends. • Low-Scale Regimes (a < 50): During periods of uncertainty or sudden news shocks (e.g: 2024-2025), the dominant scale abruptly collapses to the lower regis ter. In these regimes, and price action is almost entirely dictated by short-term fluctuations (for e.g: noise and reactionary trading). Figure 2.8: Wavelet transformation Figure 2.9: Dominant time scales plot SOICT-HUST Stock Price Analysis 15 2.2 Exploratory Data Analysis 2.2.1 Market versus Stock Betas & CAPM risk Detailed formulation: 4.12 and 4.7 Analyzing the rolling Beta (figure 2.10) insights into FPT’s risk profile over time: • Defensive Baseline: The empirical distribution of the 20-day rolling Beta reveals a median value of 0.85. Because this is less than the market baseline (β = 1.0), FPT is generally characterized as a defensive asset. On average, it exhibits less volatility than the broader VNINDEX, cushioning portfolios during market downturns. • Regime-Dependent Volatility: Despite its defensive median, the time-series plot of the rolling Beta demonstrates significant non-stationarity. FPT’s systematic risk fluctuates significantly, dropping near 0.0 (highly idiosyncratic movement discon nected from the market) and occasionally spiking above 2.5 (extreme systematic sensitivity). This indicates that FPT’s market exposure is highly regime-dependent; during specific macroeconomic shocks or sector-wide momentum shifts, FPT can temporarily abandon its defensive nature and behave as a highly aggressive, high beta stock. 2.2.2 Market-level trend drawdown & Regime classification Detailed formulation: 4.7 and 4.5 The VNINDEX serves as the primary proxy for Vietnamese market sentiment. By evaluating the index’s historical drawdowns alongside its momentum-based trend strength, we can explicitly categorize the market into distinct behavioral regimes, providing vital context for downstream predictive algorithms. Analyzing the historical trajectory of the VNINDEX through these lenses (Figure 2.11) reveals several structural insights: • Cyclical and Severe Drawdowns: The drawdown dynamics illustrate a market susceptible to deep, systemic corrections. The visualization clearly isolates two major crisis periods: the acute, rapid crash in early 2020 (approaching a-40% drawdown) and the prolonged, grinding bear market of 2022, which reached similar depths of capital destruction. • Momentum and Regime Shifts: The Trend Strength indicator effectively trans lates moving-average crossovers into a continuous oscillator, cleanly segmenting the timeline. Prolonged positive zones (such as late 2020 through 2021) represent sustained bull regimes characterized by strong, persistent upward momentum and SOICT-HUST Stock Price Analysis 16 Figure 2.10: Illustration of FPT CAPM risk & Beta distribution highly rapid recoveries from minor dips. Conversely, the deep negative troughs per fectly capture the structural bear regimes. • Transitional Market Phases: Beyond just bull and bear markets, the regime classification identifies periods of macro-level indecision. During years like 2019 and stretches of 2024, the trend strength oscillates tightly around the zero line, repre senting sideways, low-momentum environments where mean-reversion dynamics are more likely to dominate over trend-following momentum. 2.2.3 Vol-regime Z-scores & Volatility term structure The visualizations are in Figure 2.12. Volatility Term Structure Dynamics Formulation: see 4.8, for fat tail figure, vol_regime_z is just Z-score of vol_20. The 5-day volatility acts as a highly sensitive, noisy proxy for immediate market reaction. As seen in the time-series plot, there are multiple periods where the 5-day volatility violently spikes and breaks away from the smoother 20-day baseline. These SOICT-HUST Stock Price Analysis 17 Figure 2.11: Macro drawdown & Regime classification massive divergences serve as early warning signals of acute market panic and sudden liquidity shocks. Fat-Tail Risk and Z-Score Distribution The empirical distribution of Vol Z-scores provides a crucial warning regarding market risk assumptions: • Pronounced Positive Skew (Asymmetry): The histogram is not normally dis tributed; the majority of the data clumps to the left of the mean. This confirms that the stock market spends the vast majority of its time in a calm, low-volatility state, often associated with slow, grinding upward trends. • TheFat Right Tail: The most critical insight from the distribution is the existence of a "fat" right tail. A significant density of observations extends far beyond the +2 standard deviation "panic threshold," with extreme events reaching +4 or even +6 standard deviations, proving that extreme market shocks happen far more frequently than standard Gaussian statistics would predict. SOICT-HUST Stock Price Analysis 18 Figure 2.12: Vol term structure & Fat tail analysis 2.2.4 Mean Reversion & Trend Consistency The visual analysis relies on three primary engineered indicators: • Momentum Z-Score: The 20-day price return is standardized using a 20-day rolling mean and rolling standard deviation. This normalizes the momentum into a Z-score, where values exceeding ±2 standard deviations theoretically indicate statistical anomalies (overbought or oversold conditions). • Local Drawdown: Measures the percentage drop from the highest close observed over the previous 20 days, capturing the severity of localized market breakdowns. Insights and Market Dynamics Based on the generated plots, several insights regarding the market structure can be observed: Efficacy of Mean Reversion Signals: Figure 2.13 demonstrates that the benchmark index exhibits strong mean-reverting tendencies on a 20-day horizon. The momentum SOICT-HUST Stock Price Analysis 19 Z-score frequently oscillates between the +2 (overbought) and −2 (oversold) thresholds. Notably, extreme breaches of the −2Z lower bound (e.g., the liquidity shock in early 2020 and the sustained downtrend in late 2022) identify short-term exhaustion points. These extreme readings consistently precede sharp corrective rallies or structural market bottoms, validating the Z-score as a robust predictive feature for contrarian modeling strategies. Trend Instability and Drawdown Correlations: Figure 2.14 illustrates the relation ship between Trend Consistency and Local Breakdowns. The 20-day win rate is highly volatile, frequently crossing the 0.5 (50%) baseline, indicating that short-term price action is highly stochastic and rarely sustains prolonged unidirectional streaks. Furthermore, pe riods of severe 20-day local drawdowns (indicated by the deep red shaded regions) strongly correlate with trend consistency plunging well below the 0.4 level. This suggests that ma jor market corrections in this index are driven by persistent negative daily returns (a sustained lack of "up days") rather than isolated, single-day crash events. Figure 2.13: Mean reversion signals: Momentum Z-scores Figure 2.14: Trend consistency with Local breakdowns SOICT-HUST Stock Price Analysis 20 2.2.5 Stock-Level Trend Oscillators and Bounded Percentile Met rics To extract multi-scale momentum signals and identify trend reversals for the asset, we analyze the structural behavior of the Moving Average Convergence Divergence (MACD) indicator and its normalized variants across a multi-year horizon (2021 to mid-2025). The feature formulations are in 4.17. Momentum Histogram Dynamics and Velocity Acceleration The MACD histogram (Ht = MACDt−Signalt) isolates the distance between the core trend line and its slower moving average. Rather than mapping the trend direction itself, the histogram acts as a proxy for the second derivative of price, capturing market velocity and directional acceleration. An analysis of the green (bullish) and red (bearish) momentum waves across the timeline yields several insights for short-horizon forecasting: • Leading Indicator Properties (Momentum Deceleration): The histogram (figure 2.15) serves as a leading indicator for structural price turning points. As seen in the mid-2023 and mid-2024 expansions, the green bullish histogram blocks reach their peak amplitude and begin to slope downward before the absolute price peak is reached and before a formal bearish crossover trigger occurs. This shrinking of the green bars signifies a loss of buying velocity (negative acceleration). • High-Frequency Mean Reversion via Histogram Percentiles: In Figure 2.16, the teal line representing the 20-day histogram percentile (hist_percentile_20) exhibits a much higher cycling frequency than the smoother MACD line percentile. Because the histogram shifts overextended values back toward zero rapidly, its per centile tracks localized overbought and oversold states with high sensitivity. Figure 2.15: MACD vs. Signal line SOICT-HUST Stock Price Analysis 21 Figure 2.16: Bounded Percentiles Analysis 2.2.6 RSI vs. Price vs. Stochastic Momentum To evaluate structural momentum exhaustion and directional reliability, we analyze multi-scale oscillator dynamics through Relative Strength Index (RSI) and Stochastic Momentum tracking, alongside engineered indicators for signal quality and divergence (See 4.2.2). Time-Frequency Duality in Oscillators (RSI vs. Stochastic %K) The Figure 2.17 demonstrates a clear time-frequency structural decoupling between the two indicators: • High-Frequency Volatility of Stochastic %K: The Stoch_K indicator (orange line) acts as a high-frequency oscillator, rapidly oscillating across its entire domain . It reaches extreme overbought (≥ 80) and oversold (≤ 20) thresholds fre quently. This behavior captures localized closing price placement relative to the recent 14-day high-low range, making it highly sensitive to short-horizon mean reversion waves but noisy during sustained trends. • Low-Pass Smoothing of RSI(14): In contrast, the RSI_14 indicator (blue line) functions as a smoother, lower-frequency momentum tracker. It filters out minor microstructure noise and remains bounded within intermediate ranges for extended periods. • Conjoint Extremes as Regime Exhaustion Triggers: A powerful predictive feature occurs when both oscillators reach extreme saturation thresholds simul taneously. For instance, in mid-2023, both the blue and orange lines hit extreme upper boundaries (> 80), flagging a robust, highly overextended bullish regime. Conversely, when both collapse simultaneously to the lower register (as seen in deep market troughs), it indicates high-probability capitulation zones where selling ve SOICT-HUST StockPriceAnalysis 22 locity is statisticallyexhausted.Otherwise,whentheirdirections contradict, the momentumhasbeenweakenedandlessreliable. MomentumReliabilityandStructuralDivergenceMetrics Thefeaturemomentum_qualityiscomputedas:LetCROC,t∈{−1,0,1}representthe ROCdirectionalconsistencyindicatorattimet,derivedfromthealignmentofshort-and medium-termhorizons.LetMc,tdenotethemomentumcompositescore,andσMc,t signify its20-dayrollingstandarddeviation.Toaccountforinstitutional liquidityvalidation,the volumeratioVratio,t isdefinedas: Vratio,t= Vt 1 20 19 i=0 Vt−i (2.7) whereVt istherawtradingvolumeattimet. Weutilizean indicator functionI(·) that evaluates to1 if the interior condition is satisfiedand0otherwise.Toensureboundedstability fordownstreammachine learn ing inputs, thecomposite rawscore is clippedwithinthedomain .Dependingon theavailabilityofmarket liquiditydata,MQt is computedviaaconditional piecewise framework: MQt=    clip 0.3CROC,t+0.4I(|Mc,t|>σMc,t)+0.3I(Vratio,t>1) , ifvolumeisavailable, clip 0.5CROC,t+0.5I(|Mc,t|>σMc,t) , ifvolumeisunavailable. (2.8) whereclip(x)=max(0,min(1,x)). TheFigure2.18illustratesthestabilityandstructuralalignmentofthesemomentum wavesusingtwoengineeredfeatures:momentum_qualityandRSI_price_divergence. •RegimeValidationviaMomentumQuality:Themomentum_quality(navy blue line) indicator rapidlymovesbetweendiscretestructural levels (0.0,0.5,1.0). Whenitpinsat1.0, itconfirmsahigh-conviction,broad-basedtrend,givingdown streammachine learningmodelsaclearsignal totrusttrend-followingrules.Con versely,whenitplummetsto0.0, itwarnsthemodel thatthecurrentpriceaction lacksvolumeorconsistency,signalinganoisyorrangingenvironment. •DivergenceCaptureasaTurningPointPredictor:TheRSI_price_divergence indicator(darkorangeline)quantifiesdirectionalmismatchesbetween14-dayprice returnsand14-dayRSIadjustments.Itoperatesasadistinctphaseshifterstepping between+1.0,0.0,and−1.0: SOICT-HUST Stock Price Analysis 23– Value of 0.0: Indicates complete structural agreement between price momen tum and oscillator momentum.– Spikes to ±1.0: Represent hidden structural anomalies. As observed in late 2023 and early 2025, persistent jumps to extreme divergence thresholds appear right before major trend corrections or trend reversals. Bullish divergence (< 0) means decreasing sell force, whereas bearish divergence (> 0) indicates building selling pressure. Figure 2.17 Figure 2.18: RSI price divergence and momentum quality indicators 2.2.7 Stock Market Structure and Volatility Compression To model localized phase transitions and anticipate explosive directional expansions, we map the geometric boundaries of the asset’s price action. By establishing non-parametric support and resistance channels based on rolling extrema over a lookback window of w = 20 days, we extract structural covariates that capture breakout intensity and non linear volatility cycles. SOICT-HUST Stock Price Analysis 24 Dynamic Market Structure and Breakout Intensity The architectural envelope of the asset’s price is defined by the previous 20-day high and low, constructing a dynamic horizontal corridor (figure 2.19). Analyzing the distri bution of prices relative to these boundaries reveals distinct structural regimes: • Structural Consolidation and Range Trading: From mid-2021 through mid 2023, the asset is trapped in a protracted horizontal baseline between $40 and $60. During this phase, the price repeatedly tests the boundaries without sustaining a breakout, keeping the range position feature oscillating symmetrically. • Persistent Trend Extension: Beginning in mid-2023 and continuing throughout 2024, a powerful structural shift occurs. The price consistently overrides the trailing resistance line, generating a series of consecutive upside breakouts (breakout_high_strength_20 > 0, highlighted in lime green). • Structural Breakdown Regime: In early 2025, after peaking near $130, the mar ket structure flips abruptly. The price plunges through the trailing 20-day support floor, triggering a severe downside breakdown phase (breakout_low_strength_20 > 0, highlighted in crimson). This transition signals some oversell and a fundamental breakdown of the medium-term uptrend. The Volatility Squeeze and Equilibrium Expansion A core principle of market microstructure is that periods of extreme volatility compres sion act as precursors to structural expansions. To capture this phenomenon mathemati cally, we track the normalized width of the local channel via the structure_tightness_20 metric, alongside its localized 60-day statistical deviation (tightness_z). The time-series visualization (figure 2.20) of this tightness profile reveals predictive behaviors: • Coiled Energy States (The Squeeze): When the channel width collapses signif icantly below its rolling average, the Z-score crosses the threshold of tightness_z < −1.5. This triggers an extreme compression state, visualized as orange vertical "Squeeze" blocks. These episodes represent temporary market equilibriums where buyers and sellers are tightly matched. • Predictive Anchor for Regime Shifts: Examining the alignment between the two figures demonstrates that these extreme compression zones systematically pre cede major, high-velocity price moves. Notable squeeze triggers appear in mid-2022, late 2022, and late-2024 right before the massive structural breakout. SOICT-HUST Stock Price Analysis 25 Figure 2.19: Stock price structure with Resistance & Support (Zoomed in) Figure 2.20: Stock price tightness 2.2.8 Stock-Level Trend Strength and Reliability We evaluate FPT’s directional behavior by analyzing the first derivative of its expo nential moving average (Trend Velocity) alongside its rolling non-parametric directional persistence (Trend Consistency). The visualizations are in Figure 2.21. Trend Velocity and Moving Average Derivatives This feature models the momentum of the 20-day EMA using a 5-day (ema_slope_20_5) and 10-day (ema_slope_20_10) lookback shift. Because these metrics calculate the rate of change of an already smoothed baseline, they filter out high-frequency microstructural noise, exposing the true velocity of structural shifts: • Velocity Acceleration Regimes: The green shaded expansions show periods where the fast velocity line rises above the zero threshold, indicating an accelerating uptrend. Strong, sustained clusters of positive velocity are highly visible during the structural bull markets of 2020-2022 and the aggressive extension phases throughout 2023-2024. SOICT-HUST Stock Price Analysis 26 • Asymmetric Downward Shocks:Thered shaded regions isolate periods of struc tural deceleration and negative velocity. During major liquidity crises—such as the early 2020 COVID crash, the late 2022 global bear market, and the sharp early 2025 reversal—the fast velocity line violently plunges below −0.010. This reveals that downward velocity in FPT’s trend profile operates with much greater sudden ness and intensity than upward acceleration. • Crossover Signal Lags: The interaction between the fast blue line and the slow orange dashed line acts as an effective internal momentum stabilizer. When the fast velocity line crosses back toward the zero baseline while the slow line remains extended, it provides downstream models with a clear indicator of momentum de celeration prior to an actual price reversal. Trend Consistency and Win-Rate Probability Bounds This feature quantifies the structural persistence of the asset’s trajectory. By com puting a rolling 20-day mean of positive daily return counts, this feature acts as a local win-rate probability index, standardizing directional momentum into a strictly bounded domain: • Empirical Probability Boundaries: The win rate is highly non-random, oscil lating reliably within a structured envelope between a lower floor of ∼ 20% and an upper ceiling of ∼ 75%. • Persistence as a Regime Anchor: During powerful structural trends, the win rate stays pinned above the neutral 50% baseline for consecutive months. These green-filled regimes reveal a market with strong positive drift, where daily gains consistently outnumber daily losses, implying trend-following instead of mean re versions. • Capitulation Floors: Conversely, during macro market liquidations, the win rate collapses down to the 20% to 30% threshold. These deep red troughs capture periods of extreme oversold capitulation. Historically, when FPT’s 20-day win rate hits this structural floor (as seen in mid-2018, early 2020, late 2021, and early 2025), it marks a high-probability boundary where selling exhaustion is achieved. 2.2.9 Risk Regime Analysis We evaluate FPT’s structural risk architecture by tracking the dynamics of the Average True Range (ATR) alongside the Downside Volatility Ratio across the 2021–2025 timeline. SOICT-HUST Stock Price Analysis 27 Figure 2.21: Trend velocity & reliability Intraday and Gap Risk Tracking via ATR Dynamics The first plot 2.22 decouples the absolute price-normalized trading range (atr_pct) from its short-term historical baseline (atr_rel). Analyzing the interaction between these two metrics yields several insights: • Scale-Normalized Risk Context: The absolute ATR percentage (black line) demonstrates that FPT’s typical daily trading range shifts between a calm base line of 1% to 2% of the stock price and extreme historical stress levels exceeding 5% to 6%. This slow-moving baseline shift captures structural changes in market liquidity and capitalization over multiple years. • Volatilty Expansion Shocks: The Relative ATR (orange line) normalizes these shifts by evaluating the current 14-day window against a 20-day macro baseline. Periods where the orange line violently pierces the +1.5 threshold ("High Volatility Expansion") capture sudden, high-velocity regime changes. • Intraday Noise Separation: Notably, the relative ATR spikes can occur when the absolute ATR percentage is low (e.g., mid-2023 and early 2024). This provides the forecasting models with an early-warning breakout filter, flagging moments where SOICT-HUST Stock Price Analysis 28 trading ranges are expanding aggressively relative to the immediate past, indepen dent of long-term price inflation. Risk Asymmetry and Toxic Volatility Fractions The second plot 2.23 calculates the proportion of total variance attributed exclusively to negative return days (downside_vol_ratio). • Pervasive Downside Dominance: The crimson line oscillates primarily within an elevated channel between 0.4 and 0.7, revealing that FPT’s total volatility is consistently heavily influenced by downward price action. • The 0.7 Danger Zone Threshold: The horizontal dashed baseline at 0.7 delin eates the "Danger Zone" where downside volatility compromises more than 70% of the asset’s total variance. The red-shaded peaks ("Dominant Downside Risk") mark moments of severe structural decay. These episodes map to major market ca pitulations—specifically in mid 2021, late-2022, and a dense, persistent cluster in early-to-mid 2025. Figure 2.22: Gaps/Intra-day risk by ATR% Figure 2.23 SOICT-HUST Stock Price Analysis 29 2.3 Time Series Decomposition Analysis 2.3.1 Motivation Time series decomposition was investigated as a preliminary step to determine whether the FPT stock price series could be represented as a combination of interpretable compo nents such as trend, seasonality, and irregular fluctuations. If stable trend and seasonal structures existed, a decomposition-based hybrid forecasting framework could be con structed by modeling each component separately and subsequently combining the fore casts. For an additive decomposition model, the observed series can be expressed as yt = Tt +St +Rt (2.9) where Tt denotes the trend component, St denotes the seasonal component, and Rt represents the residual or irregular component. To evaluate the existence of meaningful seasonal patterns in FPT stock prices, several decomposition techniques were examined, including Classical Seasonal Decomposition, Seasonal-Trend Decomposition using Loess (STL), and Singular Spectrum Analysis (SSA). Classical Decomposition and STL Analysis To investigate whether the FPT stock price series contains meaningful seasonal pat terns, both Classical Seasonal Decomposition and Seasonal-Trend Decomposition using Loess (STL) were applied. Since financial time series rarely exhibit obvious periodic be havior, multiple candidate seasonal periods were examined, including short-term cycles (5, 10, and 20 trading days) and longer-term cycles (30, 60, and 120 trading days). For the classical decomposition approach, the time series was decomposed into trend, seasonal, and residual components under different seasonal assumptions. Figure 2.24 sum marizes the decomposition results obtained using the seasonal_decompose method. SOICT-HUST Stock Price Analysis 30 Figure 2.24: Classical seasonal decomposition of the FPT stock price series under repre sentative seasonal assumptions. Visual inspection indicates that the extracted seasonal components are relatively weak compared with the long-term trend and irregular fluctuations. Moreover, the seasonal patterns vary considerably across different candidate periods and fail to exhibit consistent recurring structures. These observations suggest that any apparent seasonality is likely driven by random market movements rather than genuine deterministic cycles. To provide a more quantitative assessment, STL decomposition was subsequently ap plied and the seasonal strength metric proposed by Hyndman and Athanasopoulos was computed: FS = max 0,1− Var(Rt) (2.10) Var(St + Rt) where values close to 1 indicate strong seasonality and values close to 0 indicate weak seasonal effects. The seasonal strength was evaluated across all candidate periods. Figure 2.25 presents the resulting seasonal strength values obtained from STL decomposition. SOICT-HUST Stock Price Analysis 31 Figure 2.25: Seasonal strength (FS) estimated from STL decomposition across multiple candidate seasonal periods. The results consistently indicate weak seasonality. Across all tested periods, the sea sonal strength remains below 0.2, implying that the extracted seasonal components ex plain only a small proportion of the total variance in the series. Furthermore, no dominant period emerges from the analysis, indicating the absence of a stable recurring cycle. The findings obtained from both Classical Decomposition and STL lead to the same conclusion: the FPT stock price series does not exhibit sufficiently strong deterministic seasonality to justify decomposition-based forecasting. Consequently, traditional decom position approaches were not considered suitable as the primary decomposition stage for the proposed forecasting framework. Singular Spectrum Analysis (SSA) Because both Classical Decomposition and STL rely on predefined seasonal assump tions, an additional experiment was conducted using Singular Spectrum Analysis (SSA), a non-parametric decomposition technique capable of extracting latent structures without requiring an explicit seasonal period. SSA consists of four major steps: 1. Embedding the original time series into a trajectory matrix; 2. Applying Singular Value Decomposition (SVD) to the trajectory matrix; 3. Grouping singular components according to their contribution; 4. Reconstructing the series from selected eigentriples. Unlike traditional decomposition methods, SSA does not assume a fixed trend-seasonal structure and can identify low-frequency and high-frequency components directly from the data. SOICT-HUST Stock Price Analysis 32 The decomposition results obtained from SSA were noticeably more informative than those produced by Classical Decomposition and STL. The first reconstructed components captured the dominant long-term dynamics of the stock price, while higher-order com ponents represented short-term oscillations and stochastic fluctuations. In particular, the reconstructed trend component appeared smoother and more stable than those obtained from conventional decomposition techniques. The decomposition reveals that a substantial proportion of the total variance is con centrated within the first few principal components, while the remaining components primarily capture noise-like behavior and localized fluctuations. This separation provides a clearer representation of the underlying structure of the FPT stock price series. From an exploratory perspective, SSA offers a more effective decomposition of financial time series than methods based on predefined seasonal assumptions. However, despite producing visually meaningful trend and noise separation, SSA does not reveal a stable and interpretable seasonal mechanism. Therefore, SSA was primarily used as an exploratory analytical tool rather than as a preprocessing stage for the final forecasting framework. Limitations of SSA for Hybrid Forecasting Although SSA produced visually meaningful decompositions, several limitations pre vented its adoption as the decomposition stage of the final hybrid forecasting framework. First, the reconstructed SSA components do not possess direct economic interpre tation. Unlike classical trend and seasonal components, individual SSA components are mathematical constructs derived from singular vectors and therefore cannot be readily associated with specific market mechanisms. Second, SSA decomposition is sensitive to several hyperparameters, particularly the embedding dimension and component grouping strategy. Different parameter selections may yield substantially different reconstructed components, reducing the robustness and reproducibility of the decomposition. Third, SSA may introduce information leakage when applied improperly in forecast ing settings. Since decomposition is often performed using the entire available sample, reconstructed components may inadvertently incorporate future information that would not be available in a real-time forecasting environment. This can lead to overly optimistic performance estimates. Finally, despite producing a cleaner separation between low-frequency and high-frequency structures, SSA did not reveal a stable and interpretable seasonal mechanism. The domi nant components primarily reflected long-term trends and stochastic market fluctuations rather than recurring seasonal cycles that could be modeled independently. For these reasons, SSA was considered an exploratory analytical tool rather than a preprocessing stage for the final forecasting architecture. SOICT-HUST Stock Price Analysis 33 2.3.2 Discussion The decomposition experiments provide important insights into the statistical charac teristics of the FPT stock price series. Both Classical Decomposition and STL indicate that seasonal effects are weak and unstable, as evidenced by seasonal strength values consistently below 0.2. These findings suggest that deterministic seasonality contributes little to the overall variation of stock prices. SSA successfully identifies latent trend structures and separates noise components more effectively than STL. However, the extracted components lack strong interpretability and do not support a reliable decomposition-based forecasting framework. Overall, the decomposition analysis suggests that FPT stock prices are primarily driven by trend dynamics, stochastic fluctuations, and volatility clustering rather than stable seasonal behavior. This observation is consistent with the stationarity tests, return distribution analysis, and volatility analysis presented in previous sections. Consequently, subsequent forecasting models focus on return-based representations, lagged features, volatility-aware indicators, and machine learning methods instead of decomposition-based hybrid forecasting approaches. SOICT-HUST Stock Price Analysis 34 Chapter 3 Statistical Hypothesis Testing and In ference This chapter validates the statistical assumptions behind the forecasting framework. The analysis focuses on FPT stock, VN30, and VNINDEX, and is organized into three main parts: methodology, hypothesis testing results, and modeling conclusions. The tests help determine whether the data should be modeled in price or return form, whether volatility requires special treatment, and which market or technical variables are statisti cally useful for prediction. 3.1 Methodology The hypothesis testing procedure follows a consistent decision rule. For each hypothe sis, a null hypothesis H0 and an alternative hypothesis H1 are defined. The statistical test produces a test statistic and a p-value. At the significance level α = 0.05, H0 is rejected if p < 0.05; otherwise, there is insufficient evidence to reject H0. The dataset contains daily market observations from 2020 to 2024. The main variables used in this chapter are FPT closing price, FPT logarithmic return Rt = ln(Pt/Pt−1), VN30 return, VNINDEX return, trading volume, and derived technical indicators. The methodology is divided into three hypothesis groups, each presented in a separate sub section below. 3.1.1 Group 1: Time Series Characteristics The first group evaluates whether FPT prices and returns satisfy basic assumptions for time series modeling. The Augmented Dickey–Fuller (ADF) test is used to check station arity. The Jarque–Bera test evaluates normality and fat-tailed behavior. The Ljung–Box Q-test checks whether returns contain significant linear autocorrelation. Engle’s ARCH LM test is used to detect volatility clustering and conditional heteroskedasticity. SOICT-HUST Stock Price Analysis 35 These tests are important because forecasting models should not be fitted directly to non-stationary price series without transformation. If returns are stationary but non normal and heteroskedastic, the model should use returns as the target variable and include volatility-aware components. 3.1.2 Group 2: Technical Analysis and Microstructure The second group evaluates whether trading volume and technical indicators provide statistically significant information. Granger causality is used to test whether volume predicts future FPT returns. Levene’s test is used to compare variance between high volume and normal-volume periods. Regression coefficient tests evaluate lagged-return momentum. Two-sample tests evaluate whether RSI oversold signals produce abnormal future returns, while variance tests evaluate whether Bollinger Bands squeezes are followed by volatility expansion. This group supports feature selection. A technical indicator should be treated cau tiously if it does not show significant standalone predictive power. However, even a non directional signal may still be useful if it helps identify higher-risk or higher-volatility periods. 3.1.3 Group 3: Market Index Relationships The third group evaluates the relationship between FPT and broad market indices. A CAPM-style regression estimates the systematic risk coefficient β between FPT and VNINDEX. Granger causality tests whether VN30 leads FPT returns. A coefficient com parison test checks whether FPT reacts asymmetrically to market upturns and downturns. A paired t-test evaluates whether FPT outperforms VN30 on average. Finally, a Pear son correlation test evaluates whether VNINDEX trading volume is associated with FPT volatility. These tests determine whether market-index variables should be included as exogenous predictors in later forecasting models such as ARIMAX, XGBoost, or hybrid models. 3.2 Hypothesis Testing Results This section reports the empirical results for 15 hypotheses. To keep the chapter struc ture clear, each hypothesis group is presented as a separate subsection: Group 1 for time series characteristics, Group 2 for technical and microstructure signals, and Group 3 for market-index relationships. SOICT-HUST Stock Price Analysis 36 3.2.1 Group 1: Time Series Characteristics of FPT This group tests whether FPT price and return series are appropriate for statistical forecasting. The results are summarized in Table 3.1. Table 3.1: Hypothesis Tests: Time Series Characteristics ID Hypothesis/Test Stat p-value Reject H0 Conclusion 1 Stationarity of FPT price (ADF) 2 Stationarity of FPT re turn (ADF) 3 Normality of FPT re turn (Jarque–Bera) 4 Autocorrelation of re turns (Ljung–Box) 5 Volatility (ARCH LM) clustering −0.0514 0.954 −32.3825 < 0.001 885.13 10.50 162.26 <0.001 0.398 <0.001 No Yes Yes No Yes FPT price is non-stationary and contains a unit root. FPT return is stationary and suitable as a modeling target. Returns are non-normal and fat-tailed. No significant linear auto correlation is detected. Strong ARCH effect and volatility clustering exist. The results indicate that raw FPT prices are non-stationary and therefore unsuitable as a direct target for predictive modeling. In contrast, FPT log returns exhibit clear stationarity, making them more appropriate for forecasting tasks. The distributional analysis further reveals strong deviations from normality, with the Jarque–Bera test strongly rejecting the Gaussian assumption (p-value ≈ 0) and excess kurtosis of 6.25 compared to the Gaussian benchmark of 3.0. These findings confirm that FPT returns exhibit pronounced heavy-tailed behavior, implying a higher likelihood of extreme market movements. In terms of temporal dependence, the Ljung–Box test indicates that log returns ex hibit no statistically significant linear autocorrelation (p-value > 0.05), suggesting limited effectiveness of purely mean-based linear models in capturing return dynamics. However, the Engle’s ARCH LM test strongly rejects the null hypothesis of homoskedasticity (p value < 10−29), providing overwhelming evidence of pronounced volatility clustering. This implies that the conditional variance of returns is time-varying and exhibits persistent clustering over time, even in the absence of linear dependence in the mean process. Con sequently, these results strongly motivate the use of GARCH-family models for effectively modeling and forecasting volatility dynamics in FPT returns. Given these characteristics, we recommend modeling frameworks that explicitly cap ture volatility dynamics, such as GARCH-type models, rather than purely autoregressive mean models such as ARIMA. Finally, due to the heavy-tailed nature of the return distribution, the Mean Absolute Error (MAE) is adopted as the optimization objective instead of RMSE. MAE is more robust to extreme values and outliers, which are frequent in the FPT return series, and therefore provides a more stable and representative training signal for model selection and SOICT-HUST Stock Price Analysis 37 hyperparameter tuning. 3.2.2 Group 2: Technical Analysis and Microstructure Signals This group evaluates whether volume, momentum, RSI, and Bollinger Bands provide useful information for forecasting. The results are summarized in Table 3.2. Table 3.2: Hypothesis Tests: Technical Analysis and Microstructure ID Hypothesis/Test Stat p-value Reject H0 Conclusion 6 Volume-price Granger causality 7 Volume spikes and volatility 8 Lag-1 return momen tum 9 RSI oversold T+3 re turn 10 Bollinger squeeze and volatility F-test min 0.129 Levene: 137.16 < 0.001 βLag1 = 0.0205 0.360 RSI< 30: 0.94% 0.214 Levene: 6.04 0.993 No Yes No No No Trading volume does not significantly predict future FPT returns. High-volume days have about 4.70× higher return variance. Lag-1 return does not sig nificantly predict next-day return. RSI oversold signals are not statistically superior. Squeeze periods do not sig nificantly expand five-day volatility. The results indicate that most standalone technical indicators do not provide statisti cally reliable predictive power for return direction. Trading volume does not Granger-cause returns, lagged momentum signals are not statistically significant, and traditional oscil lators such as RSI and Bollinger Band-based signals fail to exhibit consistent predictive effects at the 5% significance level. A more nuanced picture emerges when analyzing specific market conditions. Although the RSI oversold condition (RSI < 30) is associated with higher subsequent T+3 average returns (0.94% compared to 0.31% under normal conditions), this difference is not statis tically significant due to limited sample size and high variance, suggesting that RSI-based mean reversion signals should not be used in isolation. Similarly, Bollinger Band squeeze conditions (defined as extremely narrow bandwidth below the 5th percentile) do not lead to a statistically significant increase in subsequent return volatility. Instead, FPT prices tend to remain in prolonged low-volatility regimes following such compression periods before a clear directional move emerges. In contrast, the most robust and economically significant result is observed in volume based anomalies. Days with abnormal trading volume (exceeding 2× the 20-day moving average) exhibit approximately 4.7 times higher return variance compared to normal days, with a near-zero p-value. This finding strongly confirms that volume spikes are primarily a risk and volatility signal rather than a direct predictor of return direction. SOICT-HUST Stock Price Analysis 38 Overall, these results suggest that technical indicators in this setting are more infor mative for volatility and regime detection than for directional return forecasting. 3.2.3 Group 3: Market Index Relationships This group examines whether VNINDEX and VN30 provide useful external informa tion for explaining or forecasting FPT returns. The results are summarized in Table 3.3. Table 3.3: Hypothesis Tests: Market Index Relationships ID Hypothesis/Test 11 Systematic risk CAPM beta 12 VN30 Granger causal ity on FPT 13 Asymmetric market impact 14 Outperformance ver sus VN30 15 VNINDEX liquidity and FPT volatility Stat β =0.9562 F-test min ∆β =0.0028 Paired t-test p-value Reject H0 Conclusion <0.001 0.070 0.966 0.003 Pearson r = 0.0228 0.156 Yes No No Yes No FPT has a strong sys tematic relationship with VNINDEX (R2 =46.6%). VN30 does not Granger cause FPT returns at the 5% level. FPT beta is symmetric in market upturns and down turns. FPT significantly out performs VN30 by about +0.0755% per day. Market liquidity is not sig nificantly correlated with FPT volatility. The market relationship tests show that VNINDEX is an important explanatory vari able for FPT. The CAPM beta is highly significant and close to one, meaning that FPT moves strongly with the market. However, VN30 does not significantly lead FPT returns at the 5% level, and FPT’s beta does not differ between bullish and bearish regimes. The paired test shows that FPT significantly outperforms VN30 on average, while VNINDEX volume does not explain FPT volatility. 3.3 Conclusion and Modeling Implications The hypothesis testing results provide several important conclusions for the forecasting framework developed in later chapters. 3.3.1 Summary of Statistical Findings Across the 15 hypotheses, six results are especially important. First, FPT price is non stationary, so raw prices should not be used directly as the main target without transfor mation. Second, FPT returns are stationary, making them more appropriate for time series modeling. Third, return normality is rejected, meaning that the model should account for SOICT-HUST Stock Price Analysis 39 fat tails and outliers. Fourth, volatility clustering is strongly significant, supporting the inclusion of GARCH-type models or volatility-related features. Fifth, abnormal volume is associated with substantially higher variance, making it useful for risk detection. Sixth, VNINDEX has a strong and significant relationship with FPT returns, so market-index variables should be considered as exogenous predictors. 3.3.2 Implications for Feature Selection The tests suggest that not all technical indicators should be treated equally. RSI oversold signals, Bollinger squeeze signals, lag-1 return momentum, and trading volume alone do not show strong standalone predictive power for return direction. Therefore, these variables should not be interpreted as reliable independent trading signals. They may still be useful when combined with other variables in nonlinear models, but their individual statistical evidence is weak. In contrast, volume spikes and VNINDEX returns provide stronger evidence. Volume spikes are useful for identifying high-volatility periods, while VNINDEX returns capture systematic market movement. These variables should be prioritized in the feature engi neering stage. 3.3.3 Implications for Forecasting Models The modeling pipeline should use return-based targets rather than raw prices. Because the return distribution is fat-tailed, robust objectives such as MAE, Huber loss, or quantile loss are more appropriate than purely Gaussian-error assumptions. Since volatility clus tering is significant, volatility-aware models such as GARCH, hybrid ARIMA–GARCH, or machine learning models with rolling volatility features are justified. For exogenous variables, VNINDEX should be included because it explains a substan tial share of FPT return variation. VN30 may be included as a supplementary market feature, but the evidence for a direct leading effect is weaker. Overall, the statistical tests support a forecasting design that combines stationary return targets, robust training cri teria, market-index information, and explicit volatility modeling. SOICT-HUST Stock Price Analysis 40 Chapter 4 Forecasting Model Development 4.1 Problem Formulation The forecasting task is formulated as a supervised learning problem in time series analysis. Given a sequence of historical financial observations, the objective is to pre dict future market movements over Let Xt denote the input feature vector constructed from past observations, and yt+h denote the target variable at forecasting horizon h. The learning objective can be expressed as Xt =(xt−w,xt−w+1,...,xt−1) → yt+h (4.1) where w is the lookback window size and h is the forecasting horizon. Since the original closing price series is generally non-stationary, directly forecasting future prices may lead to unstable model performance. As stated in Hypothesis 1, the log-return series exhibits stronger stationarity properties than the raw closing price series, making it a more suitable target for supervised forecasting models. Based on the validation of Hypothesis 1 through stationarity tests, we therefore define the forecasting target as the future log return rather than the raw closing price. The target variable is computed as yt+h = rt+h = log(Pt+h) − log(Pt) = log Pt+h Pt , (4.2) where Pt denotes the closing price at time t. The model is trained to predict the future log return rt+h. During inference, the predicted log return is transformed back to the original price scale through the inverse logarithmic operation: ˆ P ∗t+h=Ptexp(ˆr∗t+h), (4.3) where ˆr∗t + h is the predicted log return and ˆP∗t + h is the reconstructed forecasted price. SOICT-HUST Stock Price Analysis 41 4.2 Data Representation and Feature Engineering In financial time series forecasting, particularly for the Vietnamese stock market (e.g., indices like VNINDEX, VN30 and individual equities such as FPT), raw price data (OHLCV) is highly noisy (low signal-to-noise ratio) and exhibits non-stationarity. To address this challenge, Feature Engineering serves as a critical phase to extract structural signals, momentum, volatility, and market relationships, thereby providing high-value pre dictive representations for machine learning (XGBoost) and deep learning (LSTM, GRU) models. The feature engineering workflow in this study is structured into three main compo nents: Market Features, Stock Features, and the Data Processing & Pipeline. 4.2.1 Market Features This group of features captures the macro state and general trend of the broad market using the two major benchmarks of the Vietnamese stock market: VNINDEX and VN30. Incorporating market features enables the predictive models to recognize the prevailing market regime and adapt their individual stock forecasts accordingly. • Market Momentum & Trend: The market trend is quantified using rates of change (momentum) across different rolling lookback windows (w ∈ {5,10,20} days): Market_mom_wt = Pmarket,t −Pmarket,t−w Pmarket,t−w (4.4) Additionally, a bullish market regime flag is defined by the crossover of short- and long-term Exponential Moving Averages (EMA): Market_bullt = I(EMA10(Pmarket)t−1 > EMA20(Pmarket)t−1) The standardized trend strength of the market is expressed as: Market_trend_strengtht = EMA10,t − EMA20,t EMA20,t +ϵ (4.5) (4.6) To measure the peak-to-trough decline over a rolling 20-day horizon, the market drawdown is calculated as: Market_drawdownt = Pmarket,t − maxi∈ Pmarket,t−i maxi∈ Pmarket,t−i + ϵ (4.7) If the drawdown drops below-5%, the binary indicator Market_deep_drawdown is activated to signal extreme systemic risk. SOICT-HUST Stock Price Analysis 42 • Market Volatility: Market price volatility is measured by the rolling standard deviation of daily log returns, annualized by multiplying by √252: σmarket,w,t = std(rmarket,) × √ 252 (4.8) To flag periods of market panic or extreme volatility, a high volatility regime indi cator is triggered when the short-term volatility exceeds its long-term average by 10%: Market_is_high_vol_regimet = I(σmarket,20,t > 1.1 × MA20(σmarket,20)t) (4.9) Furthermore, the asymmetry between upside and downside market volatility is cap tured using Downside Volatility and Volatility Asymmetry: downside_vol_20t = std({rmarket,τ | rmarket,τ < 0,τ ∈ }) × √ 252 (4.10) vol_asymmetryt = downside_vol_20t σmarket,20,t + ϵ (4.11) • Stock-Market Beta & Relative Strength: The dynamic correlation between the individual stock and the market is represented by a rolling 20-day Beta coefficient (β20): βw,t = Cov(rstock,rmarket) Var(rmarket) + ϵ (4.12) The stability of the Beta coefficient is defined as its relative variation over the last 10 days: Beta_stabilityt = std(β20) |mean(β20)| + ϵ (4.13) Relative Strength (RS) measures whether the stock is outperforming or underper forming the broad market benchmark: w−1 Relative_Strength_wt = 4.2.2 Stock Features i=0 w−1 rstock,t−i − i=0 rmarket,t−i (4.14) Stock-level features focus on describing the price action, volatility structure, and range dynamics of the individual security. This group is categorized into several technical sub classes: • Trend & Moving Averages: We employ EMAs at short, medium, and long-term horizons (w ∈ {5,10,20}). The relative distance between the closing price and the SOICT-HUST Stock Price Analysis 43 EMA provides a local overbought/oversold indicator: price_ema_dist_wt = Closet − EMAw(Close)t EMAw(Close)t + ϵ The EMA slope measures trend acceleration: ema_slope_w_st = EMAw(Close)t −EMAw(Close)t−s s ×(Closet +ϵ) (4.15) (4.16) • MACD(Moving Average Convergence Divergence): MACD calculations are adapted to the specific forecast horizon h (for instance, when h = 5, the optimized configuration is set to fast = 5,slow = 15,signal = 5): MACDt = EMAfast(Close)t −EMAslow(Close)t Signalt = EMAsignal(MACD)t Histt = MACDt − Signalt (4.17) (4.18) (4.19) To allow models to learn divergence boundaries scale-invariantly, these components are normalized by dividing by the closing price (macd_pct, hist_pct). • Momentum & Oscillators:– RSI (Relative Strength Index): RSI is calculated over 7-day and 14-day win dows. To transform threshold boundaries non-linearly (helping tree and linear models partition the space), we apply a smoothed sigmoid function: RSI_overbought_smootht = RSI_oversold_smootht = 1 1 +e−0.2(RSI14,t−70) 1 1 +e0.2(RSI14,t−30) (4.20) (4.21)– Stochastic Oscillator: The %K line indicates the relative position of the closing price within the High-Low range of the past 14 days: Stoch_Kt = 100 × Closet − mini∈ Lowt−i maxi∈ Hight−i − mini∈ Lowt−i + ϵ (4.22)– Momentum Composite: To create a robust, noise-reduced momentum signal, we combine multiple standardized Rate of Change (ROC) features: mom_compositet = 0.3ROC5,t σROC5,t + 0.4ROC10,t σROC10,t + 0.3ROC20,t σROC20,t (4.23) • Market Structure & Range Position: These features track the current price po SOICT-HUST Stock Price Analysis 44 sition relative to dynamic support and resistance levels across multiple timeframes: range_position_wt = Closet − mini∈ Closet−i maxi∈ Closet−i − mini∈ Closet−i + ϵ (4.24) The breakout strength quantifies the percentage deviation of the current price be yond the previous period’s high/low: breakout_high_strength_wt = max Closet −High_prev_w High_prev_w +ϵ ,0 (4.25) • Volatility & Risk: This includes historical volatility, downside volatility, Average True Range percentage (atr_pct) to measure price dispersion relative to market price, and Volatility of Volatility (vol_of_vol_20) to capture the uncertainty of risk. • Return Lags & Distribution: Lags of past log returns model autocorrelation structure, while rolling higher-order distribution moments such as Skewness, Kur tosis, and Quantiles (quantile 25%, quantile 75%) capture the fat-tailed return dis tributions typical of financial assets. 4.2.3 Data Processing & Pipeline To ensure features are mathematically appropriate for model input, avoid look-ahead bias, and improve convergence during training, the data pipeline implements the following systematic steps: 1. Target Construction: The target variable (yt) is defined as the cumulative log return over the forecast horizon h: yt = ln Closet+h Closet (4.26) Using log returns guarantees time-additivity and shifts the distribution of the target variable closer to normality. 2. Safe Rolling & EWM Operators:Toprevent missing data gaps (due to holidays, trading halts) from propagating NaN values across rolling computations, we deploy specialized safe rolling operations (safe_rolling and safe_ewm) with a minimum data parameter min_pct = 0.8. This requires at least 80% valid observations in the window to return a value. 3. Leakage Validation: To eliminate look-ahead bias, we execute automated corre SOICT-HUST Stock Price Analysis 45 lation checks between features at time t and future targets yt+k (where k ≥ 1): ρk = Corr(Xi,t,yt+k) (4.27) If any feature displays a future correlation |ρk| > 0.3 for k ≥ 1, the pipeline flags it for investigation. 4. Warm-up Period Handling:Rollingindicators (especially 20-day or 252-day met rics) require sufficient historical context for initialization. A warm-up period of 252 trading days (approx. one business year) is discarded at the start of the dataset before model partitioning to remove initial NaN values. 5. Feature Selection & Collinearity Mitigation: Given an initial feature space exceeding 300 engineered indicators, a three-stage feature selection pipeline was employed to identify a compact, non-redundant, and predictive feature subset for each forecast horizon h ∈ {1,5,10}. Stage 1– Importance Ranking via Gradient Boosting.AnXGBoostregressor was trained on the full feature set using a chronological (non-shuffled) train/test split to preserve temporal causality and prevent look-ahead bias. Feature importance was computed using the gain-based criterion, and the top 20–30 features were retained as candidates for each horizon. Stage 2– Pairwise Collinearity Filtering. To mitigate multicollinearity– which is known to destabilize both tree-based importance estimates and the weight estima tion of downstream models such as MLP and linear baselines– a Pearson correlation matrix was computed over the candidate feature subset. For any pair of features ex ceeding an absolute correlation threshold of |r| > 0.85, the feature with the lower XGBoost importance score was discarded, retaining the more predictive represen tative of each correlated cluster. Stage 3– SHAP-based Validation. To verify the robustness of the retained feature set and detect residual cases where a single feature within a correlated group disproportionately dominates the importance signal (a known artifact of tree-based gain importance), the model was retrained on the filtered subset and SHAP (SHapley Additive exPlanations) values were computed on the held-out test set. The mean absolute SHAP value was used as a second, model-agnostic ranking criterion, and the consistency between gain-based importance and SHAP rankings was used as a stability check. This procedure was applied independently to each forecast horizon, yielding horizon specific feature subsets of 16–18 features after collinearity filtering (detailed in Ta ble 4.1). To support a unified modeling pipeline across all three horizons, a con SOICT-HUST Stock Price Analysis 46 (a) h = 1 day (b) h = 5 days (c) h = 10 days Figure 4.1: SHAP summary plots of the selected features for forecasting horizons of 1, 5, and 10 trading days. Features are ranked by mean absolute SHAP value, indicating their overall contribution to model predictions. The variation in feature rankings across horizons highlights the horizon-dependent nature of predictive signals in financial markets. solidated set of 20 features was further derived by aggregating per-horizon SHAP rankings– features consistently ranked highly across multiple horizons were priori tized, with horizon-specific high-impact features added to complete the final set. Based on the SHAP rankings obtained across the three forecasting horizons, a con solidated set of 20 features was selected for the final modeling pipeline. Features that consistently exhibited high SHAP importance across multiple horizons were priori tized, while a small number of horizon-specific predictors were retained to preserve predictive information unique to particular forecasting windows. The selected features collectively capture trend, momentum, volatility, distributional characteristics, price positioning, and broader market regime information, provid ing a compact yet informative representation of market dynamics for downstream forecasting models. 6. Data Splitting & StandardScaler: Data is divided chronologically to preserve the temporal properties of financial series and prevent leakages from future to past. The dataset split ratios are: Train (80%), Validation (10%), and Test (10%). Z-score normalization is applied to each feature: Xscaled = X −µtrain σtrain (4.28) The scaling statistics (µtrain and σtrain) are computed exclusively on the Train set, and then applied to transform the Train, Validation, and Test sets. This guarantees no future information from Validation/Test leaks into model training. SOICT-HUST StockPriceAnalysis 47 Table4.1:SummaryofSelectedEngineeredFeatures FeatureName FeatureGroup MathematicalDefinition Predictive Pur pose close Price Currentclosingpriceofthestock Baselineassetvalua tion. vol_10 StockVolatility Annualized10-dayrollingreturn standarddeviation Captures short-term volatility. ema_20 StockTrend 20-dayExponentialMovingAv erageofprice Identifies medium termtrend. RSI_price_corr_20 StockMomentum 20-day Pearson correlation be tweenRSI-14andprice Measures diver gence/alignment of momentum. return_q25_20 ReturnDistribution Rolling25thpercentileofreturns over20days Captures downside tailrisk. return_q75_20 ReturnDistribution Rolling75thpercentileofreturns over20days Captures upside growthpotential. return_max_15 ReturnDistribution Maximumreturnover a rolling 15-daywindow Capturespositiveex tremeshocks. return_std_10 StockVolatility 10-dayrollingstandarddeviation of logreturns Quantifies return dispersion. return_mom_10_20 StockMomentum Mean(R)10−Mean(R)20 Shorter- vs longer term momentum crossover. dist_to_high_3 RangeStructure (Close−Max3,t−1)/Max3,t−1 Distanceto3-daylo calresistance. dist_to_high_5 RangeStructure (Close−Max5,t−1)/Max5,t−1 Distanceto5-daylo calresistance. downside_vol_10 StockVolatility 10-dayrollingsemi-standardde viationofnegativereturns Focusesondownside risk. downside_vol_20 StockVolatility 20-dayrollingsemi-standardde viationofnegativereturns Focuses on interme diatedownsiderisk. vn30_beta_20 MarketRelation 20-day rolling Beta coefficient relativetoVN30Index Captures systemic riskrelativetolarge caps. vnindex_trend_strength MarketTrend TrendstrengthofVNINDEXin dex((EMA10−EMA20)/EMA20) Market trend envi ronment indicator. vnindex_vol_asymmetry MarketVolatility Downside-to-totalvolatilityratio ofVNINDEXindex Marketriskasymme tryindicator. vn30_vol_10 MarketVolatility 10-dayrollingvolatilityofVN30 Index(annualized) Volatility in the blue-chip market segment. vn30_is_high_vol_regime MarketVolatility Flag if VN30 volatility exceeds long-termaverageby10% Identifies market turbulenceregimes. breakout_low_strength_10 RangeStructure max((Min10,t−1 − Close)/Min10,t−1,0) Strength of support breakouts over 10 days. return_cumsum_20 ReturnDistribution Cumulative log returnover the past20days Intermediate-term priceperformance. return_min_10 ReturnDistribution Minimumreturn over a rolling 10-daywindow Captures negative extremeshocks. SOICT-HUST Stock Price Analysis 48 4.3 Model Selection 4.3.1 Summary of Selected Features Table 4.1 summarizes the selected core features utilized in model training. To establish a robust predictive framework for financial time series forecasting, we eval uate and compare models across three paradigms: classical statistical models, ensemble based machine learning approaches, and deep learning architectures. This diverse selection allows us to compare parametric baselines against non-parametric estimators capable of modeling complex non-linear patterns. 4.3.2 Classical Models Classical econometric models serve as parametric baselines. They rely on formal sta tistical assumptions about the underlying data generating process, specifically modeling linear autocorrelation and time-varying variance structures. • ARIMA (Autoregressive Integrated Moving Average): ARIMA is the stan dard parametric model for forecasting stationary univariate time series. For a dif ferenced series Yt = (1 − B)dXt, where B is the backshift operator (BXt = Xt−1) and d is the order of integration, the model ARIMA(p,d,q) is formalized as: ϕ(B)Yt = c+θ(B)ϵt (4.29) where ϕ(B) = 1− p i=1 ϕiBi represents the autoregressive (AR) polynomial of order p, θ(B) = 1+ q j=1 θjBj represents the moving average (MA) polynomial of order q, and ϵt ∼ WN(0,σ2) is a white noise process representing random innovations. In this study, ARIMA is fit directly on the stationary log returns (d = 0), leveraging past returns to capture short-term linear dependencies. • GARCH (Generalized Autoregressive Conditional Heteroskedasticity): Financial return series commonly exhibit volatility clustering, where high-volatility periods group together, violating the homoskedasticity assumption of standard re gression. The GARCH(p,q) model addresses this by modeling the conditional vari ance σ2 t as an autoregressive process of past squared residuals and past conditional variances: rt = µt +ϵt, ϵt = σtzt, zt ∼ i.i.d.N(0,1) q σ2 t = ω + i=1 p αiϵ2 t−i + j=1 βjσ2 t−j (4.30) (4.31) SOICT-HUST Stock Price Analysis 49 where ω > 0, αi ≥ 0, and βj ≥ 0 are parameters to ensure positive conditional variance, and αi+ βj <1 guarantees covariance stationarity. GARCH captures the time-varying volatility dynamics and fat-tailed distribution profiles inherent in asset returns. 4.3.3 Machine Learning Models Machine learning models are non-parametric, relaxing linear assumptions to capture complex non-linear feature interactions and high-dimensional relationships. • RandomForest (RF):RandomForest is an ensemble bootstrap aggregation (bag ging) model composed of a collection of randomized decision trees. For regression, it reduces variance without increasing bias by averaging the predictions of M inde pendent trees: M ˆ fRF(x) = 1 M m=1 Tm(x;Θm) (4.32) where Θm represents the parameter set (split variables, split points, and terminal node values) of the m-th tree trained on a bootstrap sample of the training data. At each node split, a random subset of features is evaluated, which decorrelates the trees and increases robustness against overfitting. • XGBoost (Extreme Gradient Boosting): XGBoost is an efficient, scalable im plementation of gradient-boosted decision trees. Unlike bagging, it trains trees se quentially to minimize a regularized objective function: n Obj(t) = i=1 l(yi, ˆy(t−1) i +ft(xi)) + Ω(ft) (4.33) where l is the loss function measuring the deviation of the prediction at step t (ˆy(t−1) i +ft(xi)) from the target yi. The regularization term Ω(ft) penalizes model complexity to prevent overfitting: Ω(ft) = γT + 1 2λ T j=1 w2 j (4.34) where T is the number of terminal leaves and w represents leaf weights. XGBoost handles collinearity and tabular interactions extremely well, using a second-order Taylor expansion to optimize the objective function. SOICT-HUST Stock Price Analysis 50 4.3.4 Deep Learning Models Deep learning models leverage neural network architectures to automatically learn hi erarchical representations from sequential inputs without requiring manual feature align ment over time. • LSTM (Long Short-Term Memory): LSTM is a gated Recurrent Neural Net work (RNN) designed to mitigate the vanishing gradient problem when capturing long-term temporal dependencies in sequence data. It introduces a cell state Ct and three gating mechanisms (forget gate ft, input gate it, and output gate ot): ft = σ(Wf · + bf) it = σ(Wi · + bi) ˜ Ct = tanh(WC · + bC) Ct = ft ⊙Ct−1 +it ⊙ ˜Ct ot = σ(Wo · + bo) ht = ot ⊙tanh(Ct) (4.35) (4.36) (4.37) (4.38) (4.39) (4.40) where σ is the sigmoid activation, ⊙ represents element-wise multiplication, and ht is the hidden state. In our implementation, the final hidden state of the LSTM sequence h(−1) n is extracted and fed into a fully connected prediction head containing a Layer Normalization step, a ReLU activation, and a Dropout layer to output the predicted log return. • GRU(Gated Recurrent Unit): GRU is a streamlined variant of the LSTM that merges the cell state and hidden state, and combines the forget and input gates into a single update gate zt, alongside a reset gate rt: zt = σ(Wz · + bz) rt = σ(Wr · + br) ˜ ht = tanh(W · +bh) ht = (1 −zt)⊙ht−1 +zt ⊙˜ ht (4.41) (4.42) (4.43) (4.44) With fewer parameters than LSTM, GRU is less prone to overfitting on smaller financial datasets and trains faster while achieving comparable representation ca pacity. Similar to the LSTM, the last hidden state h(−1) n projection head to yield the final forecast. is processed through a SOICT-HUST Stock Price Analysis 51 4.4 Hyperparameter Optimization Due to the extremely low signal-to-noise ratio in financial data, predictive models are highly sensitive to hyperparameter configurations. Suboptimal settings can lead to severe overfitting or underfitting. To address this, we implement a systematic hyperpa rameter optimization (HPO) framework using **Optuna**, a state-of-the-art Bayesian optimization framework. 4.4.1 Optimization Methodology Our framework utilizes the Tree-structured Parzen Estimator (TPE) sampler as its core search engine. TPE is a sequential model-based optimization (SMBO) algorithm that models the probability of hyperparameters belonging to two distinct distributions: one yielding objective values above a certain threshold (good configurations), and one yielding values below (poor configurations). The sampler dynamically updates these prob ability distributions after each trial, prioritizing regions of the search space that maximize expected improvement. As established by Hypothesis 3, the Mean Absolute Error (MAE) computed on recon structed closing prices provides a more appropriate evaluation criterion than RMSE for practical forecasting applications, as it is less sensitive to extreme prediction errors and better reflects the typical magnitude of forecast deviations. Consequently, the hyperpa rameter optimization process is designed to minimize the validation MAE of the recon structed closing prices rather than metrics computed directly on log returns or RMSE based objectives. The objective metric evaluated for each trial is the reconstructed validation MAE: MAEreconstructed = 1 N N i=1 |Pi,actual − Pi,pred| (4.45) By evaluating error directly on price levels, the optimization process accounts for com pounding effects and market scaling. 4.4.2 Hyperparameter Search Spaces For each model family, we define a structured search space targeting parameters that control learning dynamics, model capacity, and regularization. • Recurrent Architectures (LSTM & GRU): The recurrent models’ capacity is determined by the size and depth of their hidden layers, while generalization is controlled by dropout rates and learning steps. SOICT-HUST Stock Price Analysis 52– Hidden Size (hidden_size): Categorical variable ∈ {16,32,64,128}, governing the size of the hidden state vectors.– Number of Layers (num_layers): Integer range , controlling the stacking depth of the recurrent cells.– Dropout (dropout): Range (categorical for LSTM, uniform float for GRU), regularizing connections between recurrent layers.– Learning Rate (lr): Log-uniform range , adjusting the optimization steps of the Adam optimizer.– Batch Size (batch_size): Categorical variable ∈ {16,32,64,128}, adjusting gra dient estimation resolution. • Gradient Boosting (XGBoost): XGBoost tuning focuses on finding a balance between individual tree complexity, the total number of trees, and stochastic regu larization parameters.– Estimators (n_estimators): Integer range , controlling the number of boosting iterations.– Max Depth (max_depth): Integer range , limiting the maximum depth of individual decision trees.– Learning Rate (learning_rate): Log-uniform float range , scaling the contribution of each subsequent tree (shrinkage).– Subsample (subsample): Uniform float range , representing the fraction of training instances sampled stochastically per tree.– Column Sample (colsample_bytree): Uniform float range , representing the fraction of features sampled stochastically per tree.– Minimum Child Weight (min_child_weight): Integer range , representing the minimum sum of instance weight needed in a child node to allow further partitioning. 4.4.3 Summary of Search Space Parameters Table 4.2 provides a comprehensive overview of the search parameters, their data types, search intervals, and their primary role in model regularisation. SOICT-HUST StockPriceAnalysis 53 Table4.2:HyperparameterSearchSpaceSpecifications Model Parameter Type Search Space / Range Theoretical Pur pose LSTM/GRU hidden_size Categorical {16,32,64,128} Controlsmodel rep resentationcapacity. num_layers Integer Adjustsmodeldepth to learnhierarchical temporal features. dropout Float/Cat Prevents co adaptation of weights in recur rentunits. learning_rate Log-Float Governs themagni tudeof gradientup dates. batch_size Categorical {16,32,64,128} Controls gradient variance during training. XGBoost n_estimators Integer Controls the ensem ble capacity (boost ingrounds). max_depth Integer Restricts the inter actiondepthof fea tures. learning_rate Log-Float Restricts step up datestopreventvari anceinflation. subsample Float Introduces instance bagging to prevent overfitting. colsample_bytree Float Decorrelatestreesby columnbagging. min_child_weight Integer Restricts tree split tingbasedonsample coverage. SOICT-HUST Stock Price Analysis 54 Chapter 5 Model Evaluation and Conclusion 5.1 Forecasting Performance Evaluation This chapter evaluates the forecasting performance of the proposed forecasting frame work using three machine learning and deep learning models: XGBoost, LSTM, and GRU. The evaluation is conducted on the FPT stock dataset under multiple forecasting hori zons. In addition to traditional forecasting error metrics, statistical significance tests and confidence interval analysis are performed to assess the reliability and robustness of the obtained results. 5.1.1 Experimental Setup Following the feature engineering and feature selection stages described in Chapter 4, the final feature set is used to construct supervised learning samples through a sliding window framework. Given a lookback window of size w, the forecasting task can be for mulated as: Xt =, yt = f(Xt) Three forecasting horizons are considered: • One-day ahead forecasting (h = 1) • Five-day ahead forecasting (h = 5) • Ten-day ahead forecasting (h = 10) (5.1) For XGBoost, LSTM, and GRU models, Min-Max normalization is applied to the training data: x′ = x−xmin xmax −xmin (5.2) SOICT-HUST Stock Price Analysis 55 All predicted values are subsequently transformed back to the original price scale before evaluation. 5.1.2 Evaluation Metrics The forecasting models are evaluated using four commonly adopted metrics. Mean Absolute Error (MAE) MAE = 1 n n t=1 |yt − ˆyt| Root Mean Squared Error (RMSE) n RMSE = 1 n t=1 (yt − ˆyt)2 Mean Absolute Percentage Error (MAPE) MAPE = 1 n n t=1 yt − ˆyt yt Directional Accuracy (DA) ×100 DA= 1 n n t=1 I(sign(ˆyt − yt−1) = sign(yt − yt−1)) (5.3) (5.4) (5.5) (5.6) RMSE and MAE evaluate forecasting accuracy, MAPE provides a scale-independent error measure, while Directional Accuracy evaluates the ability of the model to predict market direction. 5.1.3 Forecasting Results Table 5.1 presents the forecasting performance of the three models across different forecasting horizons. “‘latex SOICT-HUST StockPriceAnalysis 56 Table5.1:ForecastingPerformanceAcrossDifferentHorizons Model Horizon RMSE MAPE MAE DA LSTM 1 2.0990(1.5686,2.6958) 1.3598%(1.0164%,1.8095%) 1.4596(1.1493,1.8388) 47.09%(47.09%,56.08%) 5 4.7720(3.833,5.954) 3.458%(2.67%,4.51%) 3.7225(3.004,4.720) 53.19%(47.9%,61.2%) 10 6.9531(5.381,8.907) 5.093%(3.87%,6.92%) 5.5050(4.317,7.237) 51.60%(47.9%,60.7%) GRU 1 2.0326(1.5886,2.5523) 1.3237%(1.0187%,1.7259%) 1.4322(1.1508,1.8087) 48.68%(48.15%,58.20%) 5 4.2769(3.296,5.450) 2.982%(2.29%,4.04%) 3.2312(2.557,4.230) 49.47%(46.3%,58.0%) 10 5.3957(4.050,6.907) 3.723%(2.80%,5.07%) 4.0676(3.140,5.354) 51.60%(47.3%,61.2%) XGBoost 1 1.9226(1.5159,2.3899) 1.2284%(0.9502%,1.5883%) 1.3332(1.0731,1.6618) 47.47%(46.97%,57.58%) 5 4.3004(3.263,5.462) 2.931%(2.14%,4.01%) 3.1623(2.389,4.192) 50.53%(46.8%,59.6%) 10 5.9617(4.452,7.607) 3.8943%(2.7273%,5.5140%) 4.3581(3.195,5.973) 52.66%(47.9%,62.8%) ARIMA 1 1.9371(1.496,2.446) 1.217%(0.94%,1.59%) 1.3222(1.065,1.662) 46.03%(46.0%,55.0%) 5 4.1738(3.188,5.334) 2.866%(2.15%,3.90%) 3.1064(2.415,4.096) 50.00%(46.8%,58.5%) 10 5.9237(4.388,7.655) 4.100%(2.96%,5.77%) 4.4401(3.314,6.005) 52.66%(48.4%,62.8%) GARCH 1 1.9384(1.497,2.448) 1.218%(0.94%,1.59%) 1.3235(1.066,1.662) 46.03%(46.0%,55.0%) 5 4.2310(3.240,5.400) 2.930%(2.22%,3.99%) 3.1755(2.492,4.175) 48.40%(45.2%,56.9%) 10 5.9454(4.401,7.689) 4.118%(2.99%,5.82%) 4.4598(3.348,6.044) 50.53%(46.3%,60.1%) “‘ SeveralobservationscanbedrawnfromTable5.1. Theforecastingresultsdemonstratethatmodelperformancevariesacrossforecasting horizons.Forthe1-dayhorizon,XGBoostachievedthelowestRMSE,whileARIMAand GARCHproducedthelowestMAEandMAPEvalues, indicatingstrongshort-termfore castingcapability.Atthe5-dayhorizon,ARIMAobtainedthelowestMAEandMAPE, whereasGRUachievedthelowestRMSE, suggestingthatrecurrentneuralnetworksare more effectiveat capturingmedium-termtemporal dynamics.For the10-dayhorizon, GRUconsistentlydeliveredthelowestRMSE,MAE,andMAPEvalues,highlightingits superiorabilitytomodel longer-termdependenciesinfinancial timeseries. Regardingdirectional accuracy, thedifferencesamongmodelswere relativelysmall, withmostvaluesremainingcloseto50 5.2 StatisticalReliabilityofForecasts Whileforecastingmetricsprovideusefulinformationregardingpredictiveperformance, statistical testingisrequiredtodeterminewhetherobserveddifferencesbetweenmodels aremeaningful. 5.2.1 BootstrapConfidenceIntervals Toevaluatetherobustnessofforecastingperformance,bootstrapresamplingisapplied tothepredictionresiduals: et=yt−ˆyt (5.7) The95 SOICT-HUST StockPriceAnalysis 57 CI95%= (5.8) Thebootstrapconfidenceintervalsreveal substantialoverlapbetweenGRUandXG Boostacrossmostforecastinghorizons.Therefore,althoughonemodelmayexhibitalower pointestimateofforecastingerror,thetrueperformancedifferencemayberelativelysmall onceestimationuncertaintyisconsidered. 5.2.2 Diebold–MarianoTest Todeterminewhetherforecastingperformancedifferencesarestatisticallysignificant, pairwiseDiebold–Mariano(DM)testsareconducted. Thenullhypothesisisdefinedas: H0 :E=0 (5.9) wheredtdenotesthelossdifferentialbetweentwocompetingmodels. Tables5.2and5.3summarizetheresultingp-values. Table5.2:Diebold–MarianoTestResults(RMSEandMAE) Horizon ModelPair RMSEp-value MAEp-value Significant 1 GRUvsLSTM 0.0063 0.0290 Yes 1 GRUvsXGBoost 0.0085 0.0156 Yes 1 LSTMvsXGBoost 0.6768 0.3372 No 5 GRUvsLSTM 0.0498 0.0484 Yes 5 GRUvsXGBoost 0.4711 0.8243 No 5 LSTMvsXGBoost 0.0360 0.0776 Partial 10 GRUvsLSTM 0.0140 0.0344 Yes 10 GRUvsXGBoost 0.3730 0.1296 No 10 LSTMvsXGBoost 0.0067 0.0498 Yes Table5.3:Diebold–MarianoTestResultsAgainstStatisticalModels Horizon ModelPair RMSEp-value MAEp-value Significant 1 GRUvsARIMA 0.0429 0.0106 Yes 1 GRUvsGARCH 0.0441 0.0116 Yes 1 ARIMAvsGARCH 0.1092 0.1204 No 5 GRUvsARIMA 0.0246 0.0022 Yes 5 GRUvsGARCH 0.0285 0.0051 Yes 5 ARIMAvsGARCH 0.0271 0.0021 Yes 10 GRUvsARIMA 0.2123 0.2807 No 10 GRUvsGARCH 0.2049 0.2676 No 10 ARIMAvsGARCH 0.1050 0.2987 No TheDiebold–Marianotestwasconductedtodeterminewhethertheobserveddiffer ences inforecastingerrorswerestatisticallysignificant.The results indicate thatGRU SOICT-HUST Stock Price Analysis 58 significantly outperformed LSTM across all forecasting horizons under both RMSE and MAE loss functions, demonstrating the effectiveness of the GRU architecture for this forecasting task. For the 1-day horizon, significant differences were identified between GRU and the competing models, while no significant differences were observed among XGBoost, ARIMA, and GARCH. This suggests that these models achieved comparable short-term forecast ing performance despite small differences in error metrics. At the 5-day horizon, GRU remained significantly different from ARIMA and GARCH, whereas the performance gap between GRU and XGBoost was not statistically significant. For the 10-day horizon, although GRU achieved the lowest forecasting errors, its performance was statistically comparable to XGBoost, ARIMA, and GARCH according to the Diebold–Mariano test. These findings highlight the importance of complementing traditional error metrics with statistical significance testing. Lower forecasting errors do not necessarily imply statistically superior predictive performance, particularly when the differences between competing models are relatively small. 5.3 Conclusion This study proposed a statistically grounded framework for Vietnamese stock price analysis and forecasting, using FPT as the main case study and VNINDEX and VN30 as market references. The results show that FPT closing prices are non-stationary, while log returns are stationary. FPT returns also exhibit heavy tails and strong volatility clustering, which supports the use of return-based modeling, robust evaluation metrics, and volatility-aware features. The project combines statistical hypothesis testing, signal processing, feature engineer ing, and predictive modeling. ARIMA/SARIMAX and GARCH-type models are used as classical baselines, while XGBoost, MLP, LSTM, and GRU are used to capture nonlinear and sequential patterns. Model performance is evaluated through error metrics, directional accuracy, statistical comparison tests, confidence intervals, and multi-horizon forecasting. Overall, the study shows that stock forecasting should be treated not only as a pre diction problem, but also as an experimental design problem. Statistical testing helps determine appropriate transformations and assumptions, while machine learning provides flexible tools for prediction. 5.4 Future Work Future work can extend this study in several directions. First, the analysis should be expanded from FPT to more Vietnamese large-cap stocks across different sectors. Sec ond, volatility-specific models such as GARCH, EGARCH, or ARIMA–GARCH hybrids SOICT-HUST Stock Price Analysis 59 should be further developed. Third, additional exogenous variables such as interest rates, exchange rates, foreign trading flows, macroeconomic indicators, and news sentiment can be added. Fourth, trading-oriented metrics such as Sharpe ratio, maximum drawdown, cu mulative return, turnover, and transaction-cost-adjusted performance should be included. Finally, model interpretability methods such as feature importance or SHAP values can be used to explain which factors drive model predictions. SOICT-HUST Stock Price Analysis 60 Bibliography G. E. P. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, Time Series Analysis: Forecasting and Control. John Wiley & Sons, 5th ed., 2015. D. A. Dickey and W. A. Fuller, “Distribution of the estimators for autoregressive time series with a unit root,” Journal of the American Statistical Association, vol. 74, no. 366a, pp. 427–431, 1979. R. F. Engle, “Autoregressive conditional heteroscedasticity with estimates of the vari ance of united kingdom inflation,” Econometrica: Journal of the Econometric Society, vol. 50, no. 4, pp. 987–1007, 1982. T. Bollerslev, “Generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, vol. 31, no. 3, pp. 307–327, 1986. E. F. Fama, “Efficient capital markets: A review of theory and empirical work,” The Journal of Finance, vol. 25, no. 2, pp. 383–417, 1970. W. F. Sharpe, “Capital asset prices: A theory of market equilibrium under conditions of risk,” The Journal of Finance, vol. 19, no. 3, pp. 425–442, 1964. T. Chen and C. Guestrin, “Xgboost: A scalable tree boosting system,” in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 785–794, ACM, 2016. S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural Computation, vol. 9, no. 8, pp. 1735–1780, 1997. K. Cho, B. van Merri¨enboer, C. Gulcehre, D. Bahdanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using rnn encoder–decoder for sta tistical machine translation,” in Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp. 1724–1734, 2014. F. X. Diebold and R. S. Mariano, “Comparing predictive accuracy,” Journal of Busi ness & Economic Statistics, vol. 13, no. 3, pp. 253–263, 1995. SOICT-HUST Stock Price Analysis 61 P. Welch, “The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans actions on audio and electroacoustics, vol. 15, no. 2, pp. 70–73, 1967. D. N. Politis and J. P. Romano, “The stationary bootstrap,” Journal of the American Statistical Association, vol. 89, no. 428, pp. 1303–1313, 1994. M. Loève, Fonctions aléatoires de second ordre. Paris: Hermann, 1948. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Chao, and H. H. Liu, “The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 454, no. 1971, pp. 903–995, 1998. A. Grossmann and J. Morlet, “Decomposition of hardy functions into wavelets of constant shape,” in SIAM Journal on Mathematical Analysis, vol. 15, pp. 723–736, SIAM, 1984. C. Torrence and G. P. Compo, “A practical guide to wavelet analysis,” Bulletin of the American Meteorological Society, vol. 79, no. 1, pp. 61–78, 1998. G. E. P. Box and G. M. Jenkins, “Time series analysis: Forecasting and control,” Holden-Day, 1976. T. Vu, “Vnstock: Python vietnamese stock market data downloader.” https:// github.com/thinh-vu/vnstock, 2024. K. Karhunen, “ ¨ Uber lineare methoden in der wahrscheinlichkeitsrechnung,” Annales Academiae Scientiarum Fennicae. Series A. I. Mathematica-Physica, vol. 37, pp. 1 79, 1947. SOICT-HUST
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