[{"url": "https://www.mdpi.com/2227-7072/14/4/90", "title": "Predicting the Volatility of Cryptocurrencies’ Returns Using High-Frequency Data: A Comparative Analysis of GARCH, EGARCH, IGARCH, GJR-GARCH, LRE, and HAR Models", "error": null, "len": 22355, "content": "Next Article in Journal / Special Issue\n\n[Augmented Finance for Climate Action: A Systematic Review of AI, IoT, and Blockchain Applications in Sustainable Finance](https://www.mdpi.com/2227-7072/14/4/91)\n\nPrevious Article in Journal\n\n[Expectations, Credibility, and the Persistence of Currency Substitution](https://www.mdpi.com/2227-7072/14/4/89)\n\nPrevious Article in Special Issue\n\n[Quantum Blockchain: A Theoretical Framework and Applications in Cryptocurrency](https://www.mdpi.com/2227-7072/13/4/220)\n\n## Journals\n\n[Active Journals](https://www.mdpi.com/about/journals) [Find a Journal](https://www.mdpi.com/about/journalfinder) [Journal Proposal](https://www.mdpi.com/about/journals/proposal) [Proceedings Series](https://www.mdpi.com/about/proceedings)\n\n[**Topics**](https://www.mdpi.com/topics)\n\n## Information\n\n[For Authors](https://www.mdpi.com/authors) [For Reviewers](https://www.mdpi.com/reviewers) [For Editors](https://www.mdpi.com/editors) [For Librarians](https://www.mdpi.com/librarians) [For Publishers](https://www.mdpi.com/publishing_services) [For Societies](https://www.mdpi.com/societies) [For Conference Organizers](https://www.mdpi.com/conference_organizers)\n\n[Open Access Policy](https://www.mdpi.com/openaccess) [Institutional Open Access Program](https://www.mdpi.com/ioap) [Special Issues Guidelines](https://www.mdpi.com/special_issues_guidelines) [Editorial Process](https://www.mdpi.com/editorial_process) [Research and Publication Ethics](https://www.mdpi.com/ethics) [Article Processing Charge](https://www.mdpi.com/apc) [Awards](https://www.mdpi.com/awards) [Testimonials](https://www.mdpi.com/testimonials)\n\n[**Author Services**](https://www.mdpi.com/authors/services)\n\n## Initiatives\n\n[Sciforum](https://sciforum.net/) [MDPI Books](https://www.mdpi.com/books) [Preprints.org](https://www.preprints.org/) [Scilit](https://www.scilit.com/) [SciProfiles](https://sciprofiles.com/) [Encyclopedia](https://encyclopedia.pub/) [JAMS](https://jams.pub/) [Proceedings Series](https://www.mdpi.com/about/proceedings)\n\n## About\n\n[Overview](https://www.mdpi.com/about) [Contact](https://www.mdpi.com/about/contact) [Careers](https://careers.mdpi.com/) [News](https://www.mdpi.com/about/announcements) [Press](https://www.mdpi.com/about/press) [Blog](http://blog.mdpi.com/)\n\n[Sign In / Sign Up](https://www.mdpi.com/user/login)\n\n## Notice\n\nYou can make submissions to other journals\n[here](https://susy.mdpi.com/user/manuscripts/upload).\n\n\n_clear_\n\n## Notice\n\nYou are accessing a machine-readable page. 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She has more than 11 years of academic and professional experience in the field of finance. Her primary research interests focus on financial risk analysis, hedge fund performance, and financial markets.\n\n\n[Read more](https://www.mdpi.com/2227-7072/14/4/90#) [Read less](https://www.mdpi.com/2227-7072/14/4/90#)\n\n\\* [![](https://pub.mdpi-res.com/img/design/orcid.png?0465bc3812adeb52?1790157138)](https://orcid.org/0009-0007-8266-3017)\n\nDepartment of Finance, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia\n\n\\*\n\nAuthor to whom correspondence should be addressed.\n\n_Int. J. Financ. Stud._ **2026**, _14_(4), 90; [https://doi.org/10.3390/ijfs14040090](https://doi.org/10.3390/ijfs14040090)\n\nSubmission received: 25 January 2026\n/\nRevised: 20 March 2026\n/\nAccepted: 25 March 2026\n/\nPublished: 3 April 2026\n\n\n\n(This article belongs to the Special Issue [Cryptocurrency and Blockchain: Opportunities and Challenges for Financial Systems](https://www.mdpi.com/journal/ijfs/special_issues/03KO97RJ82))\n\nDownload _keyboard\\_arrow\\_down_\n\n[Download PDF](https://www.mdpi.com/2227-7072/14/4/90/pdf?version=1775177977)\n\n[Download PDF with Cover](https://www.mdpi.com/2227-7072/14/4/90#)\n\n[Download XML](https://www.mdpi.com/2227-7072/14/4/90#)\n\n[Download Epub](https://www.mdpi.com/2227-7072/14/4/90/epub)\n\n[Versions Notes](https://www.mdpi.com/2227-7072/14/4/90/notes)\n\n## Abstract\n\nThis study provides a comprehensive evaluation of six volatility forecasting models applied to twelve dominant and less dominant cryptocurrencies across multiple time horizons using high-frequency intraday data. The exponential generalized autoregressive conditional heteroskedastic (EGARCH), integrated GARCH (IGARCH), standard GARCH, GJR-GARCH, lagged realized volatility (LRE), and heterogeneous autoregressive (HAR) models are systematically compared using 5 min computed return data from September 2018 to September 2020. Our analysis encompasses three forecast horizons (1-day, 7-day, and 30-day) to assess model performance under varying temporal constraints. Through univariate Mincer–Zarnowitz regressions, encompassing tests, and out-of-sample evaluation using root mean squared error (RMSE) and quasi-likelihood loss (QLIKE) functions, we identify significant performance heterogeneity across models and cryptocurrencies. The HAR model exhibits stronger predictive accuracy at short horizons, while EGARCH exhibits relatively stronger performance at longer horizons, although overall explanatory power declines as forecast horizon increases. Importantly, no single model consistently provides optimal forecasts across all cryptocurrencies. Consistent with prior evidence suggesting model performance varies across assets. Encompassing regressions reveal that combining HAR with EGARCH specifications significantly enhances explanatory power across all temporal frames. Out-of-sample Diebold–Mariano tests indicate that HAR generates the lowest forecast errors for most cryptocurrencies, though EGARCH performs exceptionally well for high-market-capitalization assets. These findings provide regime-conditional insights into horizon- and asset-specific volatility dynamics during the pre-institutionalization phase of cryptocurrency markets. The study contributes to emerging literature by incorporating less-dominant cryptocurrencies and offering robust empirical evidence on the asymmetric and persistent volatility characteristics unique to digital asset markets. These findings should be interpreted within the context of the 2018–2020 sample period, representing a pre-institutionalized phase of cryptocurrency markets, and may not fully generalize to structurally different market regimes characterized by increased institutional participation and regulatory development.\n\nKeywords:\n\n[cryptocurrency](https://www.mdpi.com/search?q=cryptocurrency); [volatility forecasting](https://www.mdpi.com/search?q=volatility+forecasting); [high-frequency data](https://www.mdpi.com/search?q=high-frequency+data); [GARCH models](https://www.mdpi.com/search?q=GARCH+models); [realized volatility](https://www.mdpi.com/search?q=realized+volatility); [HAR](https://www.mdpi.com/search?q=HAR); [EGARCH](https://www.mdpi.com/search?q=EGARCH)\n\n## 1\\. Introduction\n\nSince the seminal introduction of Bitcoin by ( [Nakamoto, 2008](https://www.mdpi.com/2227-7072/14/4/90#B33-ijfs-14-00090)), cryptocurrencies have transformed the landscape of financial innovation. Cryptocurrencies represent a novel class of non-tangible digital assets secured through cryptographic algorithms, operating independently of traditional regulatory authorities and financial intermediaries ( [Nakamoto, 2008](https://www.mdpi.com/2227-7072/14/4/90#B33-ijfs-14-00090)). These peer-to-peer electronic cash systems enable direct online payments without intermediary institutions, fundamentally altering transaction cost structures and monetary transfer mechanisms ( [Cheah & Fry, 2015](https://www.mdpi.com/2227-7072/14/4/90#B12-ijfs-14-00090)). The distinctive characteristics of cryptocurrencies—including algorithmic security, absence of government backing, and purely digital representation—have catalysed their rapid adoption as both alternative payment systems and innovative investment instruments ( [Baur et al., 2018](https://www.mdpi.com/2227-7072/14/4/90#B4-ijfs-14-00090)).\n\nThe cryptocurrency market has witnessed exponential growth, with thousands of digital currencies now available for trading. Bitcoin, first traded in 2009, remains the dominant cryptocurrency, yet a multitude of alternative coins (altcoins) have emerged, including Ethereum, Ripple, Litecoin, and others with varying market capitalizations and technological architectures ( [Catania & Sandholdt, 2019](https://www.mdpi.com/2227-7072/14/4/90#B11-ijfs-14-00090)). This diversity has attracted considerable scholarly attention, with researchers attempting to comprehend the unique behavioral patterns, pricing dynamics, and volatility characteristics that distinguish cryptocurrencies from traditional financial assets ( [Kristoufek, 2015](https://www.mdpi.com/2227-7072/14/4/90#B26-ijfs-14-00090)).\n\nVolatility forecasting represents a critical component of cryptocurrency market analysis, serving essential functions for portfolio optimization, risk management, derivative pricing, and regulatory oversight. Unlike conventional fiat currencies, cryptocurrencies exhibit extreme volatility levels, rendering accurate volatility prediction both challenging and economically consequential. The inherent volatility clustering, long memory properties, and asymmetric shock responses observed in cryptocurrency returns necessitate sophisticated econometric models capable of capturing these complex dynamics ( [Mensi et al., 2019](https://www.mdpi.com/2227-7072/14/4/90#B30-ijfs-14-00090)).\n\n\n[... middle omitted — see footer ...]\n\n\n\n## Article Metrics\n\nNo\n\nNo\n\n### Article Access Statistics\n\nFor more information on the journal statistics, click [here](https://www.mdpi.com/journal/ijfs/stats).\n\n\n\nMultiple requests from the same IP address are counted as one view.\n\n\nZoom\\| Orient \\| As Lines \\| As Sticks \\| As Cartoon \\| As Surface \\|Previous Scene\\|Next Scene\n\n## Cite\n\nExport citation file:\nBibTeX \\|\nEndNote \\|\nRIS\n\n**MDPI and ACS Style**\n\nAlsamaani, A.; Aldhahi, H.\nPredicting the Volatility of Cryptocurrencies’ Returns Using High-Frequency Data: A Comparative Analysis of GARCH, EGARCH, IGARCH, GJR-GARCH, LRE, and HAR Models. _Int. J. Financ. Stud._ **2026**, _14_, 90.\nhttps://doi.org/10.3390/ijfs14040090\n\n**AMA Style**\n\nAlsamaani A, Aldhahi H.\nPredicting the Volatility of Cryptocurrencies’ Returns Using High-Frequency Data: A Comparative Analysis of GARCH, EGARCH, IGARCH, GJR-GARCH, LRE, and HAR Models. _International Journal of Financial Studies_. 2026; 14(4):90.\nhttps://doi.org/10.3390/ijfs14040090\n\n\n**Chicago/Turabian Style**\n\nAlsamaani, Abdulrahman, and Huda Aldhahi.\n2026\\. \"Predicting the Volatility of Cryptocurrencies’ Returns Using High-Frequency Data: A Comparative Analysis of GARCH, EGARCH, IGARCH, GJR-GARCH, LRE, and HAR Models\" _International Journal of Financial Studies_ 14, no. 4: 90.\nhttps://doi.org/10.3390/ijfs14040090\n\n\n**APA Style**\n\nAlsamaani, A., & Aldhahi, H.\n\n(2026). Predicting the Volatility of Cryptocurrencies’ Returns Using High-Frequency Data: A Comparative Analysis of GARCH, EGARCH, IGARCH, GJR-GARCH, LRE, and HAR Models. _International Journal of Financial Studies_, _14_(4), 90.\nhttps://doi.org/10.3390/ijfs14040090\n\n\nNote that from the first issue of 2016, this journal uses article numbers instead of page numbers. 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raise/lower offset to page through it).\n─────────────────────────────"}, {"url": "https://spectrum.library.concordia.ca/995904/1/Sarrafshirazi_MSc_F2025.pdf", "title": null, "error": null, "len": 22090, "content": "## High-Frequency Forecasting of Bitcoin Volatility: Evaluating HAR Models with Realised\n\n## Semivariance and Jump Components\n\n## Raheleh Sarrafshirazi\n\nA Thesis In The John Molson School of Business\n\nPresented in Partial Fulfillment of the Requirements for the Degree of Master of Science (Finance) at Concordia University Montreal, Quebec, Canada\n\n## August 2025\n\n## ©Raheleh Sarrafshirazi, 2025\n\n---\n\nCONCORDIA UNIVERSITY\nSchool of Graduate Studies\n\nThis is to certify that the thesis\n\nPrepared By: Raheleh Sarrafshirazi\n\nEntitled: High-Frequency Forecasting of Bitcoin Volatility: Evaluating HAR\nModels with Realised Semivariance and Jump Components\n\nand submitted in partial fulfillment of the requirements for the degree of\nMaster of Science (Finance)\n\ncomplies with the regulations of the University and meets the accepted standards with\nrespect tooriginality and quality.\n\nSigned by the final Examining Committee:\n\nDr. Juliane Proelss Chair\n\nDr. Parianen Veeren Examiner\n\nDr. Mehmet Özsoy Examiner\n\nDr. Kun Ho Kim Supervisor\n\nApproved by Dr. Frederick Davis Graduate Program Director\n\nDean Dr. Anne-Marie Croteau\n\n---\n\n**ABSTRACT**\n\nHigh-Frequency Forecasting of Bitcoin Volatility: Evaluating HAR Models with Realised Semivariance and Jump Components\n\n## Raheleh Sarrafshirazi\n\nBitcoin’s continuous trading, speculative nature, and high volatility create distinctive challenges for risk management and forecasting. This thesis examines how high-frequency realised volatility (RV) measures and Heterogeneous Autoregressive (HAR) models capture Bitcoin’s volatility dynamics and improve forecast accuracy. Adapting RV methods from equity markets, the analysis adds downside semivariance to address asymmetric negative returns and jump variation to capture price movements. Using minute-level Bitcoin prices from, I compute RV from 5-minute returns and estimate four HAR variants—baseline HAR, HAR-RS, HAR-J, and HAR-RS-J. Models are re-estimated in a rolling window, and forecasts are evaluated with RMSE, MAE, and QLIKE. Robustness checks test stability under different data granularities and market regimes. A GARCH(1,1) benchmark provides a parametric comparison, with HAR variants outperforming it at short horizons, while GARCH exceeds performance at longer horizons. Results show that HAR-type models capture Bitcoin’s long memory, volatility clustering, and asymmetry effectively. HAR-J delivers the most accurate day-ahead, while HAR-RS leads at weekly and monthly horizons due to persistent downside risk. At quarterly horizons, forecast accuracy converges across models as high-frequency information loses relevance. This study extends RV–HAR modelling to cryptocurrency markets, revealing shorter volatility persistence and greater jump contributions than in equities. It identifies downside semivariance and continuous variation as robust predictors across different market conditions and offers horizon- specific tools—HAR-J for short-term risk management and HAR-RS for medium-term volatility planning.\n\n**Keywords:** Bitcoin Volatility, Realised Volatility, Heterogeneous Autoregressive Model, Semivariance, Jump Variation, High-Frequency Data, Volatility Forecasting, Cryptocurrency Markets, Bipower Variation, Risk Management.\n\niii\n\n---\n\n**Acknowledgements** I would like to express sincere gratitude to my supervisor, Dr. Kun Ho Kim, for his invaluable guidance and support throughout my research. His constructive feedback and unwavering availability for discussions have been instrumental in the development of this thesis. I am sincerely grateful for his kindness, encouragement, and mentorship, which have profoundly shaped my academic journey. I would also like to thank my thesis committee members, Dr. Parianen Veeren and Dr. Mehmet Özsoy, for their time, insightful comments, and constructive feedback.\n\nLastly, I would like to express my appreciation to my family, friends, and colleagues for their support and encouragement, which have been a constant source of strength throughout this journey. I am deeply grateful to everyone who has contributed to my growth and helped shape the person I am today.\n\niv\n\n---\n\nTable of Contents\n\nChapter 1 Introduction... 1\nChapter 2 Literature Review... 3\n2.1 Traditional Volatility Models ... 3\n2.2 RV and High-Frequency Data... 4\n2.3 HAR and Its Extensions... 5\n2.4 Volatility in Cryptocurrency Markets ... 6\n2.5 Model Evaluation Methods... 6\nChapter 3 Data and Preprocessing... 8\n3.1 Data Source and Timeframe... 8\n3.2 Data Quality Checks and Variable Definitions... 8\n3.3 Preprocessing... 9\n3.4 Descriptive Statistics... 9\nChapter 4 Methodology... 11\n4.1 Realized Volatility Measures ... 11\n4.1.1 Realized Volatility (RV)... 11\n4.1.2 Bipower Variation (BV)... 13\n4.2 HAR-type Volatility Models ... 14\n4.2.1 Baseline HAR-RV Specification... 14\n4.2.2 Extended HAR Variants... 15\n4.3 Estimation and In-sample Diagnostics... 16\n4.3.1 Data Partition and Horizon Mapping... 16\n4.3.2 OLS Estimation and Standard Errors... 17\n4.3.3 In-Sample Residual Diagnostics... 17\n4.4 Forecast Design and Out-of-Sample Evaluation... 18\n4.4.1 Sample Split, Estimation Window, and Forecast Horizon... 18\n4.4.2 Performance Metrics... 18\nChapter 5 Empirical Results... 20\n5.1 Preliminary Descriptive Analysis... 20\n5.2 In-Sample Estimation Outcomes... 22\n\n---\n\n5.2.1 HAR model coefficient estimates ... 23\n5.2.2 Residual Diagnostics ... 25\n5.3 Out-of-sample Forecast Evaluation ... 27\n5.4 Robustness Checks ... 29\n5.5 Comparison with GARCH Benchmarks ... 31\nChapter 6 Conclusion ... 33\n\n6.1 Key Findings at a Glance ... 33\n6.2 Academic Contributions ... 34\nChapter 7 Discussion ... 35\n\n7.1 Practical Implications ... 35\n7.2 Robustness and Market Regimes ... 36\n7.3 Limitations ... 37\n7.4 Future Research Directions ... 38\n## References ... 39\n\nvi\n\n---\n\n## List of Figures\n\nFigure 1: Daily RV aime–series ... 42\n\nFigure 2: Daily RV Distribution ... 43\n\nFigure 3: Daily RV Q-Q Plot ... 44\n\nFigure 4: Daily RV ACF/PACF ... 45\n\nvii\n\n---\n\n## List of Tables\n\naable 1: Summary Statistics for Bitcoin Price and Volatility Measures ... 46\naable 2: Summary Statistics for HAR Model Inputs ... 47\n\nTable 3: Unit-Root and Diagnostic Tests for Daily RV ... 48\n\nTable 4: Correlation Matrix of HAR Model Inputs ... 49\n\nTable 5: Estimated coefficients for HAR-type regressions of h-day-ahead RV ... 50\n\nTable 6: Pass-fail summary of in-sample residual diagnostics ... 51\n\nTable 7: Forecast Performance of HAR-Type Models ... 52\n\nTable 8: Robustness Checks for Forecast Performance ... 53\n\nTable 9: Forecast Accuracy: HAR-type Models vs. GARCH Benchmark ... 54\n\nviii\n\n---\n\n## Chapter 1 Introduction\n\nBitcoin’s emergence as a highly volatile, 24/7-traded asset has transformed financial markets and the analytical tools required to study them. Unlike traditional securities, Bitcoin operates across global exchanges without downtime, attracts diverse participants, and exhibits abrupt price jumps driven by speculative sentiment and rapid information diffusion. These features necessitate precise volatility forecasting for risk management, derivative pricing, and regulatory oversight in cryptocurrency markets. However, most studies rely on daily GARCH-type models, which overlook high-frequency data and fail to capture Bitcoin’s unique volatility dynamics, such as asymmetry, inverted leverage effects, and discrete jumps.\n\nVolatility modelling has evolved significantly over the past four decades, from Engle’s (1982) ARCH and Bollerslev’s (1986) GARCH frameworks to realised volatility (RV) approaches that leverage intraday data. In equity markets, RV-based Heterogeneous Autoregressive (HAR) models effectively capture long memory, volatility clustering, and multi-scale dynamics. Yet, few studies apply these advances to Bitcoin or incorporate RV extensions like realised semivariance or jump variation, despite their relevance to cryptocurrency-specific behaviours. This gap motivates a high- frequency approach tailored to Bitcoin’s market microstructure and behavioural drivers.\n\nThis thesis addresses three research questions: (1) Can HAR-type models based on high-frequency RV effectively capture Bitcoin’s long-memory volatility patterns? (2) Which components— downside semivariance or jump variation—add the most predictive value, and how does this vary across forecast horizons? (3) Are these results robust to changes in data granularity and market regimes, such as the post-COVID period characterized by lower volatility and increased institutional adoption?\n\nTo address these questions, I construct RV, bipower variation (BV), realised semivariance, and jump measures from 5-minute Bitcoin prices in an aggregated Kaggle dataset (August 2017– February 2025). I estimate four HAR variants—baseline HAR, HAR-RS, HAR-J, and HAR-RS- J—and, using a fixed-width rolling window equal to the initial 80 % of the sample (2,215 days), I generate out-of-sample forecasts at 1-, 7-, 30-, and 90-day horizons. Forecast accuracy is assessed with RMSE, MAE, and QLIKE. Robustness checks with 10-minute sampling and a post-COVID subsample show the model hierarchy is stable across microstructure settings and market regimes.\n\nThe dataset reflects Bitcoin’s mature trading environment post-Mt. Gox collapse and Binance’s launch, capturing key volatility episodes, including the 2018 “crypto winter,” the March 2020 COVID shock, and the 2021–2025 bull–bear cycles. This period ensures deep liquidity and modern exchange infrastructure, enabling RV measures to approximate true integrated volatility accurately.\n\nThis thesis contributes in three ways. Academically, it extends realised semivariance and jump-augmented HAR models to Bitcoin, offering new evidence on volatility dynamics in digital assets. Methodologically, it demonstrates the stability of forecast rankings across sampling frequencies and market regimes, highlighting the adaptability of HAR-type models. Practically, it provides guidance for risk management: HAR-J excels for day-ahead forecasts, while HAR-RS dominates at weekly and monthly horizons, driven by persistent downside risk.\n\nThe thesis is structured as follows. Chapter 2 reviews volatility modelling, from ARCH and GARCH to RV and HAR, emphasizing extensions relevant to cryptocurrencies. Chapter 3 describes the Bitcoin dataset, preprocessing, and descriptive statistics. Chapter 4 details the RV measures, HAR variants, and estimation strategy. Chapter 5 presents empirical results, including in-sample diagnostics, out-of-sample forecast rankings, and robustness checks. Chapter 6 summarizes key findings and academic contributions. Chapter 7 discusses practical implications, limitations, and future research directions.\n\nBy integrating high-frequency data, realised measures, and HAR-type models, this thesis bridges volatility forecasting methods from equity markets to the unique dynamics of cryptocurrency trading, delivering tools and insights tailored to Bitcoin’s volatility profile.\n\n---\n\nChapter 2 Literature Review\n\nVolatility drives critical decisions in financial markets, from managing risks to pricing derivatives and shaping investment strategies. Over time, researchers have refined their approaches to modeling volatility, moving from early parametric models to methods that harness high-frequency data. This section explores that evolution, focusing on the development of ARCH and GARCH models, their strengths and limitations, and the emergence of RV as a powerful tool for capturing price fluctuations, particularly in dynamic markets like Bitcoins.\n\n2.1 Traditional Volatility Models\n\nEarly efforts to model the changing nature of volatility began with Engle (1982), who introduced the Autoregressive Conditional Heteroskedasticity (ARCH) model, a major advance that ties a time series variance to past squared errors. Bollerslev (1986, 1987) extended this with the Generalized ARCH (GARCH) model, which became a standard for estimating and forecasting volatility. These models excel at capturing volatility clustering, where large price changes often lead to more large changes, and small changes to small ones (Cheikh et al., 2020). They also address the leverage effect, where negative returns increase volatility more than positive ones, a pattern Black (1976) identified and Bollerslev et al. (2006) and Brini and Lenz (2024) linked to market reactions to negative shocks.\n\nHowever, despite their widespread use, these models exhibit several limitations that have spurred the development of alternative approaches. ARCH and GARCH models rely on daily returns, which carry significant noise, obscuring true volatility, or integrated volatility (Patton, 2011). This noise can weaken forecast accuracy, as Andersen and Bollerslev (1998) demonstrated. GARCH models also struggle to fully capture long-memory patterns where volatility persists over time or the fat-tailed distributions typical of financial returns (McAleer and Medeiros, 2008). If researchers fail to account for structural breaks, such as sudden shifts in price variance due to external events, these models may overestimate persistence (Aharon et al., 2023). Moreover, GARCH models cannot easily incorporate intraday data, limiting their ability to analyze fine-grained market dynamics (Bollerslev et al., 2016). These limitations prompted researchers to turn to high-frequency data, leading to the rise of RV measures (Zhang et al., 2005).\n\n---\n\n2.2 RV and High-Frequency Data\n\nIn response to the discussed challenges, RV emerged as a robust, model-free method to estimate price variation using high-frequency data. Andersen and Benzoni (2008) define RV as the sum of squared returns over short intervals, typically a day, using high-frequency data. Grounded in the theory of quadratic variation (Andersen et al., 2003), RV approximates integrated volatility more accurately as sampling frequency increases in idealized markets. Unlike noisy daily squared returns, RV offers precise and stable volatility estimates, making it ideal for studying fast-moving markets like cryptocurrencies (Andersen and Benzoni, 2008; Andersen et al., 2003). This advance paves the way for more sophisticated models, such as the Heterogeneous Autoregressive (HAR) framework, which extends RV's applicability across multiple time scales.\n\nHigh-frequency data unlock precise volatility estimates, but they come with challenges. Market microstructure noise —think price discreteness, bid-ask bounces, non-synchronous trading, or data errors—can distort RV estimates, especially at very high sampling frequencies (Hansen and Lunde, 2006). This noise introduces spurious autocorrelations and biases, potentially leading to inconsistent or diverging estimates (Liu et al., 2015). To tackle this, researchers developed robust methods. Liu et al. (2015) proposed optimal and sparse sampling, Zhang et al. (2005) introduced the two-scales estimator, and Barndorff-Nielsen et al. (2004) designed kernel-based estimators to improve RV accuracy.\n\nBeyond addressing measurement noise, another line of research focuses on decomposing total volatility into its components. Barndorff-Nielsen et al. (2004) introduced bipower variation (BV), which consistently estimates the integrated variance of the continuous price path while remaining robust to jumps. By subtracting BV from RV, researchers isolate the jump component, capturing discrete price movements that often spike volatility in financial markets (Barndorff-Nielsen et al., 2004). To address asymmetry in volatility, Patton and Sheppard (2015) developed realized semivariance, splitting RV into components tied to positive and negative returns. This approach retains sign information, offering deeper insights into volatility dynamics, especially in markets like Bitcoin (Zhang and Zhao, 2023). These advancements in RV methodologies have significantly improved the accuracy of volatility measurement in high-frequency financial data, laying the\n\n---\n\n\n\n---\n\nHAR framework as a flexible and powerful tool for analyzing the distinctive volatility patterns observed in Bitcoin and other cryptocurrency markets.\n\n## 2.4 Volatility in Cryptocurrency Markets\n\n\n[... middle omitted — see footer ...]\n\n\nRegressor labels correspond to the notation in Chapter 4 ($RV_t = quarterly mean$, $RV_{om} = six-month mean$, $RV_p = yearly mean$). *, **, and *** represent 10%, 5%, and 1% levels of significance respectively. The bottom row reports the adjusted $R^2$ for each regression.\n\n$$\\begin{array}{cccccccccccccccc}\nh=1 & 7 & 30 & 90 & HAR & HAR-RS & HAR-J & HAR-RS-J & HAR-J & HAR-RS-J & HAR-J & HAR-RS-J & HAR-J & HAR-RS-J \\\\\nHAR & HAR-RS & HAR-J & HAR-RS-J & HAR-J & HAR-RS-J & HAR-J & HAR-RS-J & HAR-J & HAR-RS-J & HAR-J & HAR-RS-J & HAR-J & HAR-RS-J \\\\\n\\phi_0 & 0.3411***(0.0231) & & & & & & & & & & & & & & \\\\\n\\phi_1 & 0.2186***(0.0449) & 0.2429***(0.0442) & 0.2086***(0.0433) & 0.2425***(0.0421) & 2.0604***(0.1864) & 1.1195***(0.2075) & 1.0340***(0.2062) & 1.1051***(0.2055) & & & & & & & & \\\\\n\\phi_2 & 0.2319***(0.0536) & 0.2626***(0.0527) & 0.2163***(0.0517) & 0.1744***(0.0501) & 2.0697***(0.3424) & 2.1695***(0.3329) & 2.1315***(0.3315) & 1.9954***(0.3307) & 8.3852***(0.8262) & 6.9992***(0.8444) & 6.8015***(0.8433) & 6.7350***(0.8381) & & & & & & \\\\\n\\phi_3 & & 0.7037***(0.3499) & 0.6388*(0.3401) & 0.6611*(0.3392) & 0.7345*(0.3376) & 3.3562*(1.3106) & 3.3800*(1.3000) & 3.4224*(1.2986) & 3.4439*(1.2986) & 17.7270***(3.0654) & 15.4716***(3.0725) & 15.3231***(3.0651) & 15.8143***(3.0361) & & & & & & \\\\\n\\phi_4 & & & 0.7037*(0.3499) & 0.6388*(0.3401) & 0.6611*(0.3392) & 0.7345*(0.3376) & 3.3562*(1.3106) & 3.3800*(1.3000) & 3.4224*(1.2986) & 3.4439*(1.2986) & -24.4654***(3.0486) & -23.9101***(3.0473) & -25.1231***(3.0410) & & & & & & \\\\\n\\phi_5 & & & & -3.8380*(1.2511) & -3.6912*(1.2516) & -3.6566*(1.2527) & -3.6061*(1.2250) & -1.3929*(3.6981) & -1.6224*(3.6137) & -1.4559*(3.6022) & -0.2519*(3.5734) & & & & & & \\\\\n\\phi_6* & -0.3769***(0.0861) & -0.9277***(0.1733) & -0.8831*(0.4019) & -3.7121***(0.8386) & -0.3398*(1.1130) & -8.9116***(2.0708) & 1.6088*(2.7237) & -19.5136***(5.5705) & & & & & & \\\\\n\\phi_7* & 1.0099***(0.0802) & -2.2243***(0.2115) & 2.8566***(0.3721) & -2.8224*(1.1279) & 3.0233***(1.0285) & -10.8784***(3.2523) & 4.4646*(2.4235) & & & & & & \\\\\n\\phi_8* & 0.3155***(0.0280) & 1.9978***(0.1462) & 1.1843*(0.1320) & 4.6664***(0.7070) & 2.3597***(0.3453) & 13.2775***(2.1516) & 4.4947***(0.7542) & & & & & & \\\\\n\\phi_9* & 0.1429(0.1518) & & -1.5385*(0.7218) & & -2.5218(1.9567) & & -5.2448(5.0888) & & & & & & \\\\\n\\phi_10* & -1.2477***(0.1126) & -2.5053***(0.2260) & -2.1719***(0.5294) & -2.9702***(1.0968) & -1.9216(1.4465) & -6.3695*(2.9853) & & & & & & \\\\\nAdj.R² & 26.5% & 29.0% & 31.8% & 35.8% & 26.3% & 30.4% & 31.0% & 31.8% & 12.6% & 14.8% & 15.3% & 16.3% & 2.0% & 3.5% & 4.0% & 5.9%\n\n---\n\n\n\n---\n\nTable 7: Forecast Performance of HAR-Type Models\nThis table presents out-of-sample forecast performance for four HAR-type models across horizons $h =$\n1,7,30,90 calendar days. Forecasts are generated using the rolling-window approach over the period August\n25, 2023 – February 28, 2025. Performance is evaluated using Root Mean Squared Error (RMSE), Mean\nAbsolute Error (MAE), and the QLIKE loss function. Bold figures indicate the lowest loss per metric and\nhorizon.\n\nHorizon / Model RMSE MAE QLIKE\n$h=1$\nHAR 0.00064 0.00038 0.35926\nHAR-RS 0.00063 0.00037 0.35487\n**HAR-J** **0.00062** **0.00034** **0.32979**\nHAR-RS-J 0.00065 0.00040 137.35995\n\n$h=7$\nHAR 0.00283 0.00247 0.19349\n**HAR-RS** **0.00275** **0.00240** 0.18409\n**HAR-J** 0.00276 **0.00240** **0.18405**\nHAR-RS-J 0.00286 0.00250 369.80394\n\n$h=30$\nHAR 0.01292 0.01157 0.18959\n**HAR-RS** **0.01262** **0.01129** **0.18384**\nHAR-J 0.01268 0.01135 0.18449\nHAR-RS-J 0.01298 0.01163 0.18877\n\n$h=90$\nHAR 0.04202 0.03847 0.16259\n**HAR-RS** **0.04162** **0.03802** **0.16052**\nHAR-J 0.04173 0.03816 0.16107\nHAR-RS-J 0.04196 0.03845 0.16212\n\n---\n\nTable 8: Robustness Checks for Forecast Performance\nQLIKE loss values for the four HAR-type models under three scenarios: baseline (5-minute sampling, full sample), alternative sampling frequency (10-minute returns), and post-COVID subsample (March 15, 2020 – February 28, 2025). Forecast horizons are $h = 1,7,30,90$ calendar days. Bold values denote the lowest QLIKE for each horizon within a robustness scenario.\n\nHorizon / Model Baseline (5-min) 10-min Post-COVID\n\n$h = 1$\nHAR 0.35926 0.39051 **0.27097**\nHAR-RS 0.35487 0.39529 0.27156\nHAR-J **0.32979** **0.35666** 0.27548\nHAR-RS-J 137.35995 337.93234 0.27607\n\n$h = 7$\nHAR 0.19349 0.20112 0.13811\n**HAR-RS** 0.18409 **0.19117** **0.12882**\nHAR-J **0.18405** 0.19483 0.13154\nHAR-RS-J 369.80394 0.20739 0.13076\n\n$h = 30$\nHAR 0.18959 0.20261 0.08008\n**HAR-RS** **0.18384** **0.19677** **0.07793**\nHAR-J 0.18449 0.19901 0.07886\nHAR-RS-J 0.18877 0.20295 0.07796\n\n$h = 90$\nHAR 0.16259 0.18045 **0.02228**\n**HAR-RS** **0.16052** **0.17864** 0.02351\nHAR-J 0.16107 0.17998 0.02323\nHAR-RS-J 0.16212 0.18072 0.02261\n\n---\n\nTable 9: Forecast Accuracy: HAR-type Models vs. GARCH Benchmark\nComparison of the best-performing HAR-type model at each horizon with the best GARCH specification,\nselected by Bayesian Information Criterion (GARCH(1,1) with generalized error distribution). Out-ofsample forecasts are evaluated using MAE, RMSE, and QLIKE across horizons $h = 1, 7, 30, 90$ calendar\ndays.\n\nHorizon / Model RMSE MAE QLIKE\n$h = 1$\nHAR-J 0.00062 0.00034 0.32979\nGARCH 0.00069 0.00046 0.41559\n$h = 7$\nHAR-RS 0.00275 0.00240 0.18409\nGARCH 0.00038 0.00033 0.16737\n$h = 30$\nHAR-RS 0.01262 0.01129 0.18384\nGARCH 0.00028 0.00025 0.09975\n$h = 90$\nHAR-RS 0.04162 0.03802 0.16052\nGARCH 0.00026 0.00025 0.07110\n\n54\n\n──────── [TRUNCATED] ────────\nShowing 16,141 chars (head) + 5,477 chars (tail) of 83,829 total clean characters.\nFull text saved to: /opt/data/cache/web/spectrum.library.concordia.ca-713a9c6322.md\nTo read the omitted middle: read_file path=\"/opt/data/cache/web/spectrum.library.concordia.ca-713a9c6322.md\" offset=213 limit=200  (the file is the complete page; raise/lower offset to page through it).\n─────────────────────────────"}, {"url": "https://quantpedia.com/are-there-seasonal-intraday-or-overnight-anomalies-in-bitcoin/", "title": "Are There Seasonal Intraday or Overnight Anomalies in Bitcoin? | QuantPedia", "error": null, "len": 20644, "content": "# Are There Seasonal Intraday or Overnight Anomalies in Bitcoin?\n\n18.February 2022\n\n[bitcoin](https://quantpedia.com/tag/bitcoin/) [cryptocurrencies](https://quantpedia.com/tag/cryptocurrencies/) [market timing](https://quantpedia.com/tag/market-timing/) [own-research](https://quantpedia.com/tag/own-research/) [seasonality](https://quantpedia.com/tag/seasonality/)\n\n**At Quantpedia, we love [seasonality effects](https://quantpedia.com/quantpedias-composite-seasonalcalendar-strategy-case-study/), and our [screener includes several strategies](https://quantpedia.com/screener/?screener_tab=screener-classic&FilterKeywords=seasonality&FilterPremium=Only+Free) that exploit them. These anomalies are fascinating since they usually offer a favorable risk and reward ratio and are commonly invested only during short periods. Frequently, these strategies are valuable additions to portfolios because they are not that sensitive to overall market performance. This short article presents a brief examination of some possible Bitcoin seasonalities.**\n\n**If you are interested in [more cryptocurrency research articles, then you are invited to visit our related page](https://quantpedia.com/cryptocurrency-trading-research/), or you can subscribe to [Quantpedia Premium](https://quantpedia.com/pricing/) or [Pro](https://quantpedia.com/pricing-pro/) service, which also covers this asset class.**\n\nVideo summary:\n\nOvernight Trading in Bitcoin - Quantpedia Explains (Trading Strategies) - YouTube\n\nTap to unmute\n\n[Overnight Trading in Bitcoin - Quantpedia Explains (Trading Strategies)](https://www.youtube.com/watch?v=LdW6iP9OjN4) [Quantpedia](https://www.youtube.com/channel/UC_YubnldxzNjLkIkEoL-FXg)\n\n![thumbnail-image](https://yt3.ggpht.com/DrgZQiKM1-Fx4SCRFq4E--20MeeVqISLWPnicSDFSKb6_q9X8Bxjw-jsDkYvv6jpDhyLHUmKrQ=s68-c-k-c0x00ffffff-no-rj)\n\nQuantpedia3.61K subscribers\n\n[Watch on](https://www.youtube.com/watch?v=LdW6iP9OjN4)\n\n## Seasonality Effects in Various Asset Classes\n\nAs we observe markets, we tend to identify various patterns that continuously repeat. As one of the most followed markets, the stock market is probably connected with most of the sayings, empirical observations, seasonality research, or even some legends like “sell in May and go away.” Although some proposed seasonalities might be far-fetched, there are plenty of sound and research-backed seasonality effects. In the stock market, there is sound evidence of many seasonality anomalies, e.g., the [Turn of the Month effect](https://quantpedia.com/strategies/turn-of-the-month-in-equity-indexes/) (Xu and McConnell, 2006), [Option-Expiration Week](https://quantpedia.com/strategies/option-expiration-week-effect/) (Stivers and Sun, 2013), or [Payday Anomaly](https://quantpedia.com/strategies/payday-anomaly/) (Ma and Pratt, 2018). However, the seasonality is not stock market exclusive. There is seasonality in [Treasury bonds connected with auctions](https://quantpedia.com/strategies/seasonality-in-treasury-auctions-strategy/) (Lou et al., 2013), [annual rebalancing of the S&P GSCI index in commodities](https://quantpedia.com/strategies/front-running-sp-gsci-index/) (Yan et al., 2019), or [FOMC meetings and US dollar](https://quantpedia.com/strategies/federal-open-market-committee-meeting-effect-on-us-dollar/) (Mueller et al., 2014). Overall, plenty of seasonality effects can be connected with a specific hour, day in the week/month, or even a more extended period. Regardless of the period, all effects have one common matter: abnormal performance during the timeframe. For example, there might be a large amount of capital that investors seek to allocate that creates upward pressure and stocks rise.\n\nAll the aforementioned effects are present in the developed markets that offer a long history either for empirical observations or thorough systematic analysis. Are there any seasonality effects in Bitcoin’s market? Indisputably, the BTC has attracted many, but there is high volatility, and the market is truly dynamic. This research aims to examine some possible seasonality effects in BTC using the hourly data from the Gemini exchange during 9.10.2015 – 3.2.2022.\n\nOne of the most recognized effects relates to the part of the day – the opening of the market, closing auction, [overnight anomaly](https://quantpedia.com/strategies/overnight-anomaly/), [intraday reversal](https://quantpedia.com/strategies/intraday-reversal-in-currency-markets/), and many more daily effects were suggested by academics. However, the cryptocurrency markets are unique, and these crypto-assets are traded 24/7. Therefore, there is no “open” or “close” time. Although we can map the hours to when traditional markets are open, cryptos can still be traded outside these hours.\n\n## Main analysis\n\nIn our first examination, we map the Gemini hours to NYSE hours, and we examine the period when the NYSE is open (9:30-16:00). For BTC, we define the NYSE hours as 10:00-16:00 of NY local time (we miss half an hour to ensure that the NYSE is already open given our hourly granularity) to 15:00-21:00 UTC +0. Therefore, we define the intraday return as the return during 10:00-16:00, the overnight as return from 16:00 to 10:00 on the following day, and daily return as the return during 16:00 to 16:00 of the following day. Additionally, we define the days when the NYSE is closed (weekends and holidays) and the days when the NYSE is opened. To examine Bitcoin’s behavior, one can evaluate statistical properties, e.g., by plotting a boxplot.\n\nSecondly, by dividing returns into intraday, overnight, and daily components for days when NYSE is open or closed, one can examine the cumulative returns and empirically judge the properties during these distinct periods. Even though the crypto markets never close, defining the “intraday” and “overnight” components can be interesting since we can examine the performance when the main market is open. Additionally, it can represent the “core” daily hours when people (traders and investors) tend to be most active, at least on the traditional markets.\n\n![](https://quantpedia.com/app/uploads/2022/02/Boxplot-1024x615.png)![](https://quantpedia.com/app/uploads/2022/02/1-1024x622.png)![](https://quantpedia.com/app/uploads/2022/02/2-1024x622.png)\n\nAs expected, the most significant proportion of the overall return relates to the days when NYSE is open (there are more days like that). Several interesting properties can be observed during weekends and holidays. The intraday return is stronger and more stable than the overnight return. Conversely, this does not hold for the days when NYSE is opened. In this case, the overnight’s return dominates, and the intraday’s return is small and volatile.\n\n![](https://quantpedia.com/app/uploads/2022/02/3-1024x622.png)\n\n### **Main Takeaways**\n\nSo, what about the main takeaways? The weekends/holidays performance is driven mainly by the intraday’s component, and the overnight’s return is more volatile, at least from the US investor’s perspective. The opposite holds for the “normal” days when the NYSE is opened. The intraday return is relatively small and volatile, and the performance is driven mostly by the overnight component.\n\nWith the availability of the hourly data, we can also examine the hourly patterns in BTC. Are there significant differences during the day? Is there any period when it is best to hold the BTC? These are the questions we aim to answer in the following section.\n\n![](https://quantpedia.com/app/uploads/2022/02/4-1024x469.png)\n\nThe hourly distribution of the daily returns is not uniform. There are several periods when the return is relatively small and economically insignificant. Furthermore, there are several hours when the BTC returns are above the average. In particular, the returns for 22:00 and 23:00 seem to be the most economically significant. On the other hand, the sample’s returns for 3:00 and 4:00 are the worst.\n\n### **Which results are Significant and which are not?**\n\nNonetheless, the negative returns are insignificant, while several positive returns are statistically significant on the 5% level. From both statistical and economic points of view, the returns 22:00 and 23:00 dominate. Interestingly, all major markets are closed during this period. For UTC +0, the NYSE is open during 14:30 and 21:00, Tokyo Stock Exchange is also closed (it is opened from 00:00 to 06:00 of UTC +0 time), Hong Kong is also closed (it is opened from 01:30 to 08:00 of UTC +0 time), same as India (2:30 to 10:00 of UTC +0 time), and Australia is closed too (23:00 to 05:00 of UTC +0 time). Both London and continental Europe are closed during these significant hours since it is night there. Therefore, it seems that the best time to trade (and hold) BTC is when every other major exchange is closed.\n\n![](https://quantpedia.com/app/uploads/2022/02/5-1024x503.png)\n\nBased on the previous results, we propose a simple seasonality strategy with a simple rule: buy Bitcoin at 21:00 (UTC +0) and sell it at 23:00 (UTC +0).\n\n![](https://quantpedia.com/app/uploads/2022/02/6-1024x615.png)\n\nCompared to the BTC, the performance of the seasonality strategy is much more stable – the annualized volatility is 20.93%, and the maximum drawdown is only -22.45%. The annualized return is 33%.\n\n## Short conclusion\n\nFirstly, we identified a major discrepancy among the intraday and overnight returns during the days when the NYSE is opened or closed (weekends and holidays). When the traditional market is closed, BTC has a strong intraday component and weak overnight component, and vice versa for the days when the NYSE is opened.\n\nSecondly, we have examined the hourly patterns in Bitcoin’s return. Results also point to a systematical difference. There is no statistically negative hour, but the performance is worst during 03:00 and 04:00 (UTC +0). On the other hand, there are several hours when the BTC returns are statistically significant. The most sizeable and significant returns relate to the 22:00 and 23:00. We also show that based on this finding, it is possible to construct a simple seasonality based strategy that is invested only during the two hours of the day and can deliver sizeable annualized returns of 33% with much smaller risk than the passive BTC holding, either measured by the volatility or maximum drawdown.\n\n**Authors:**\n\n**[Matúš Padyšák](https://www.linkedin.com/in/matus-padysak-14a44b185/)**, Senior Quant Analyst, Quantpedia.com\n\n**[Radovan Vojtko](https://www.linkedin.com/in/radovan-vojtko-2aa6408/)**, CEO & Head of Research, Quantpedia.com\n\n* * *\n\n**Are you looking for more strategies to read about? [Sign up for our newsletter](https://quantpedia.com/sign-up-for-our-newsletter/) or visit our [Blog](https://quantpedia.com/blog/) or [Screener](http://quantpedia.com/Screener)**.\n\n**Do you want to learn more about Quantpedia Premium service? 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Check our list of [Algo Trading Discounts](https://quantpedia.com/links-tools/?category=algo-trading-discounts)**.\n\n* * *\n\n**Or follow us on:**\n\n**Facebook [Group](https://www.facebook.com/groups/quantstrategies), Facebook [Page](https://www.facebook.com/quantpedia/), [Twitter](https://twitter.com/quantpedia), [Linkedin](https://www.linkedin.com/company/quantpedia), [Medium](https://quantpedia.medium.com/) or [Youtube](https://www.youtube.com/channel/UC_YubnldxzNjLkIkEoL-FXg)**\n\n* * *\n\n**Related Literature**\n\nLou, Dong, Hongjun Yan, and Jinfan Zhang. “Anticipated and repeated shocks in liquid markets.” The Review of Financial Studies 26.8 (2013): 1891-1912.\n\nMa, Aixin and Pratt, William Robert, Payday Anomaly (September 28, 2018). Available at SSRN: https://ssrn.com/abstract=3257064 or http://dx.doi.org/10.2139/ssrn.3257064\n\nMueller, Philippe, Paolo Porchia, and Andrea Vedolin. “Policy Announcements in FX Markets.” London School of Economics and Political Science working paper (2014).\n\nStivers, Chris T. and Sun, Licheng, Returns and Option Activity over the Option-Expiration Week for S&P 100 Stocks (July 16, 2013). Journal of Banking and Finance, Vol. 37, pp. 4226-4240, November 2013., Available at SSRN: https://ssrn.com/abstract=1571786 or\n\nXu, Wei and Xu, Wei and McConnell, John J., Equity Returns at the Turn of the Month (July 2006). Available at SSRN: https://ssrn.com/abstract=917884 or http://dx.doi.org/10.2139/ssrn.917884\n\nYan, Lei and Irwin, Scott and Sanders, Dwight R., Is the Supply Curve for Commodity Futures Contracts Upward Sloping? (February 7, 2019). 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