IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.09722.html
   My bibliography  Save this paper

Expectile hidden Markov regression models for analyzing cryptocurrency returns

Author

Listed:
  • Beatrice Foroni
  • Luca Merlo
  • Lea Petrella

Abstract

In this paper we develop a linear expectile hidden Markov model for the analysis of cryptocurrency time series in a risk management framework. The methodology proposed allows to focus on extreme returns and describe their temporal evolution by introducing in the model time-dependent coefficients evolving according to a latent discrete homogeneous Markov chain. As it is often used in the expectile literature, estimation of the model parameters is based on the asymmetric normal distribution. Maximum likelihood estimates are obtained via an Expectation-Maximization algorithm using efficient M-step update formulas for all parameters. We evaluate the introduced method with both artificial data under several experimental settings and real data investigating the relationship between daily Bitcoin returns and major world market indices.

Suggested Citation

  • Beatrice Foroni & Luca Merlo & Lea Petrella, 2023. "Expectile hidden Markov regression models for analyzing cryptocurrency returns," Papers 2301.09722, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2301.09722
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.09722
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kristjanpoller, Werner & Bouri, Elie & Takaishi, Tetsuya, 2020. "Cryptocurrencies and equity funds: Evidence from an asymmetric multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Kim, Minjo & Lee, Sangyeol, 2016. "Nonlinear expectile regression with application to Value-at-Risk and expected shortfall estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 1-19.
    3. James W. Taylor, 2019. "Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 121-133, January.
    4. Corbet, Shaen & Meegan, Andrew & Larkin, Charles & Lucey, Brian & Yarovaya, Larisa, 2018. "Exploring the dynamic relationships between cryptocurrencies and other financial assets," Economics Letters, Elsevier, vol. 165(C), pages 28-34.
    5. Ye, Wuyi & Zhu, Yangguang & Wu, Yuehua & Miao, Baiqi, 2016. "Markov regime-switching quantile regression models and financial contagion detection," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 21-26.
    6. Sascha Mergner & Jan Bulla, 2008. "Time-varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 771-802.
    7. White, Halbert & Kim, Tae-Hwan & Manganelli, Simone, 2015. "VAR for VaR: Measuring tail dependence using multivariate regression quantiles," Journal of Econometrics, Elsevier, vol. 187(1), pages 169-188.
    8. Bouri, Elie & Molnár, Peter & Azzi, Georges & Roubaud, David & Hagfors, Lars Ivar, 2017. "On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier?," Finance Research Letters, Elsevier, vol. 20(C), pages 192-198.
    9. Luca De Angelis & Leonard J. Paas, 2013. "A dynamic analysis of stock markets using a hidden Markov model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1682-1700, August.
    10. Ji, Qiang & Bouri, Elie & Gupta, Rangan & Roubaud, David, 2018. "Network causality structures among Bitcoin and other financial assets: A directed acyclic graph approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 70(C), pages 203-213.
    11. Luca Merlo & Lea Petrella & Valentina Raponi, 2021. "Forecasting VaR and ES using a joint quantile regression and implications in portfolio allocation," Papers 2106.06518, arXiv.org.
    12. Marco Bottone & Lea Petrella & Mauro Bernardi, 2021. "Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1079-1107, September.
    13. Cheah, Eng-Tuck & Fry, John, 2015. "Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin," Economics Letters, Elsevier, vol. 130(C), pages 32-36.
    14. Zhang, Yue-Jun & Bouri, Elie & Gupta, Rangan & Ma, Shu-Jiao, 2021. "Risk spillover between Bitcoin and conventional financial markets: An expectile-based approach," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    15. Yi, Shuyue & Xu, Zishuang & Wang, Gang-Jin, 2018. "Volatility connectedness in the cryptocurrency market: Is Bitcoin a dominant cryptocurrency?," International Review of Financial Analysis, Elsevier, vol. 60(C), pages 98-114.
    16. Nikos Tzavidis & Nicola Salvati & Timo Schmid & Eirini Flouri & Emily Midouhas, 2016. "Longitudinal analysis of the strengths and difficulties questionnaire scores of the Millennium Cohort Study children in England using M-quantile random-effects regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 427-452, February.
    17. Yarovaya, Larisa & Brzeszczyński, Janusz & Lau, Chi Keung Marco, 2016. "Intra- and inter-regional return and volatility spillovers across emerging and developed markets: Evidence from stock indices and stock index futures," International Review of Financial Analysis, Elsevier, vol. 43(C), pages 96-114.
    18. Katsiampa, Paraskevi & Corbet, Shaen & Lucey, Brian, 2019. "Volatility spillover effects in leading cryptocurrencies: A BEKK-MGARCH analysis," Finance Research Letters, Elsevier, vol. 29(C), pages 68-74.
    19. Dyhrberg, Anne Haubo, 2016. "Hedging capabilities of bitcoin. Is it the virtual gold?," Finance Research Letters, Elsevier, vol. 16(C), pages 139-144.
    20. Merlo, Luca & Petrella, Lea & Raponi, Valentina, 2021. "Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation," Journal of Banking & Finance, Elsevier, vol. 133(C).
    21. Baur, Dirk G. & Hong, KiHoon & Lee, Adrian D., 2018. "Bitcoin: Medium of exchange or speculative assets?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 54(C), pages 177-189.
    22. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    23. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Gang-Jin & Xie, Chi & Wen, Danyan & Zhao, Longfeng, 2019. "When Bitcoin meets economic policy uncertainty (EPU): Measuring risk spillover effect from EPU to Bitcoin," Finance Research Letters, Elsevier, vol. 31(C).
    2. Beatrice Foroni & Luca Merlo & Lea Petrella, 2023. "Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market," Papers 2307.06400, arXiv.org.
    3. Taylor, James W., 2022. "Forecasting Value at Risk and expected shortfall using a model with a dynamic omega ratio," Journal of Banking & Finance, Elsevier, vol. 140(C).
    4. Zeng, Ting & Yang, Mengying & Shen, Yifan, 2020. "Fancy Bitcoin and conventional financial assets: Measuring market integration based on connectedness networks," Economic Modelling, Elsevier, vol. 90(C), pages 209-220.
    5. Corbet, Shaen & Katsiampa, Paraskevi & Lau, Chi Keung Marco, 2020. "Measuring quantile dependence and testing directional predictability between Bitcoin, altcoins and traditional financial assets," International Review of Financial Analysis, Elsevier, vol. 71(C).
    6. Aurelio F. Bariviera & Ignasi Merediz‐Solà, 2021. "Where Do We Stand In Cryptocurrencies Economic Research? A Survey Based On Hybrid Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 377-407, April.
    7. Li, Xingyi & Gan, Kai & Zhou, Qi, 2023. "Dynamic volatility connectedness among cryptocurrencies and China's financial assets in standard times and during the COVID-19 pandemic," Finance Research Letters, Elsevier, vol. 51(C).
    8. Kwon, Ji Ho, 2020. "Tail behavior of Bitcoin, the dollar, gold and the stock market index," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 67(C).
    9. BRIK, Hatem & El OUAKDI, Jihene & FTITI, Zied, 2022. "Roles of stable versus nonstable cryptocurrencies in Bitcoin market dynamics," Research in International Business and Finance, Elsevier, vol. 62(C).
    10. Achraf Ghorbel & Wajdi Frikha & Yasmine Snene Manzli, 2022. "Testing for asymmetric non-linear short- and long-run relationships between crypto-currencies and stock markets," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(3), pages 387-425, September.
    11. Fang, Tong & Su, Zhi & Yin, Libo, 2020. "Economic fundamentals or investor perceptions? The role of uncertainty in predicting long-term cryptocurrency volatility," International Review of Financial Analysis, Elsevier, vol. 71(C).
    12. Mensi, Walid & Sensoy, Ahmet & Aslan, Aylin & Kang, Sang Hoon, 2019. "High-frequency asymmetric volatility connectedness between Bitcoin and major precious metals markets," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    13. Andrada-Félix, Julián & Fernandez-Perez, Adrian & Sosvilla-Rivero, Simón, 2020. "Distant or close cousins: Connectedness between cryptocurrencies and traditional currencies volatilities," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 67(C).
    14. Chu, Jeffrey & Chan, Stephen & Zhang, Yuanyuan, 2021. "Bitcoin versus high-performance technology stocks in diversifying against global stock market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    15. Corbet, Shaen & Lucey, Brian & Urquhart, Andrew & Yarovaya, Larisa, 2019. "Cryptocurrencies as a financial asset: A systematic analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 182-199.
    16. Hsu, Shu-Han & Sheu, Chwen & Yoon, Jiho, 2021. "Risk spillovers between cryptocurrencies and traditional currencies and gold under different global economic conditions," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    17. Ahmed, Walid M.A., 2022. "Robust drivers of Bitcoin price movements: An extreme bounds analysis," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    18. Fang, Libing & Bouri, Elie & Gupta, Rangan & Roubaud, David, 2019. "Does global economic uncertainty matter for the volatility and hedging effectiveness of Bitcoin?," International Review of Financial Analysis, Elsevier, vol. 61(C), pages 29-36.
    19. Yi, Shuyue & Xu, Zishuang & Wang, Gang-Jin, 2018. "Volatility connectedness in the cryptocurrency market: Is Bitcoin a dominant cryptocurrency?," International Review of Financial Analysis, Elsevier, vol. 60(C), pages 98-114.
    20. Bedi, Prateek & Nashier, Tripti, 2020. "On the investment credentials of Bitcoin: A cross-currency perspective," Research in International Business and Finance, Elsevier, vol. 51(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2301.09722. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.