Advanced GARCH Specifications for Cryptocurrency Volatility Incorporating Asymmetry, Regime-Switching, and Long-Memory Effects
DOI:
https://doi.org/10.34021/ve.2025.08.02(5)Keywords:
cryptocurrency volatility, GARCH models, regime-switching, long-memory effects, volatility forecastingAbstract
Cryptocurrency markets are highly volatile, creating challenges for accurate risk management and forecasting. As digital assets become more integrated into financial systems, understanding their volatility dynamics is essential for investors and policymakers. Previous research has primarily applied standard GARCH models to cryptocurrencies, often neglecting advanced specifications that capture asymmetry, regime-switching, and long-memory effects. This limits the accuracy of volatility forecasts and fails to reflect the unique behaviour of digital assets. This study aims to identify the most effective GARCH-class models for forecasting volatility in Bitcoin, Ethereum, Binance Coin, and Ripple. We analyse daily returns from August 2017 to December 2024, applying eight advanced GARCH specifications: EGARCH, GJR-GARCH, FIGARCH, HYGARCH, MSGARCH, CS-GARCH, and Log-GARCH. Hyperparameter tuning is conducted via grid search across lag orders (p, q ∈ [1, 5]), mean equations, and error distributions. Model performance is evaluated using AIC, BIC, RMSE, and MAE. Results show that MSGARCH and EGARCH outperform symmetric and short-memory models, highlighting the importance of regime-switching and leverage effects. FIGARCH provides the best fit for Bitcoin and Ethereum, confirming long-memory persistence. Skewed Student’s t and GED distributions improve accuracy by capturing heavy tails and asymmetry. These findings demonstrate the limitations of standard GARCH models and underscore the value of advanced specifications in modelling cryptocurrency volatility. The study offers practical insights for traders and risk managers, contributing to more robust forecasting in non-stationary markets. Advanced GARCH models significantly enhance volatility prediction for digital assets. Future research could extend this framework to other speculative instruments or integrate machine learning techniques to further improve performance.
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References
1. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of variance of United Kingdom inflation. Econometrica, 50(4), 987–1008. https://doi.org/10.2307/1912773
2. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1
3. Panagiotidis, T., Papapanagiotou, G., & Stengos, T. (2022). On the volatility of cryptocurrencies. Research in International Business and Finance, 62, Article 101724. https://doi.org/10.1016/j.ribaf.2022.101724
4. De Almeida, D., & Hotta, L. K. (2014). The leverage effect and the asymmetry of the error distribution in GARCH-based models: The case of Brazilian market-related series. Pesquisa Operacional, 34(2), 237–250. https://doi.org/10.1590/0101-7438.2014.034.02.0237
5. Bouri, E., Kristoufek, L., Ahmad, T., & Shahzad, S. J. H. (2024). Microstructure noise and idiosyncratic volatility anomalies in cryptocurrencies. Annals of Operations Research, 334(1–3), 547–573. https://doi.org/10.1007/s10479-022-04568-9
6. Gupta, H., & Chaudhary, R. (2022). An empirical study of volatility in the cryptocurrency market. Journal of Risk and Financial Management, 15(11), Article 513. https://doi.org/10.3390/jrfm15110513
7. Khan, M., & Khan, M. (2021). Cryptomarket volatility in times of COVID-19 pandemic: Application of GARCH models. Economic Research Guardian, 11(2), 170–181.
8. Huang, J.-Z., Ni, J., & Xu, L. (2022). Leverage effect in cryptocurrency markets. Pacific-Basin Finance Journal, 73, Article 101773. https://doi.org/10.1016/j.pacfin.2022.101773
9. Kaseke, F., Ramroop, S., & Mwambi, H. (2022). A comparative analysis of the volatility nature of cryptocurrency and JSE market. Investment Management and Financial Innovations, 19(4), 23–39. https://doi.org/10.21511/imfi.19(4).2022.03
10. Quan, Y. X., Yang, T. X., Fei, C. Y., Cheong, C. W., & Min, L. (2023). Asymmetric volatility and risk analysis of Bitcoin cryptocurrency market. Journal of Quality Measurement and Analysis, 19(2), 73–79
11. Jiang, Z., Mensi, W., & Yoon, S.-M. (2023). Risks in major cryptocurrency markets: Modeling the dual long memory property and structural breaks. Sustainability, 15(3), 2193. https://doi.org/10.3390/su15032193
12. Harasheh, M., & Bouteska, A. (2025). Volatility estimation through stochastic processes: Evidence from cryptocurrencies. North American Journal of Economics and Finance, 75, 102320. https://doi.org/10.1016/j.najef.2024.102320
13. Cremaschini, A., Punzo, A., Martellucci, E., & Maruotti, A. (2023). On stylized facts of cryptocurrencies returns and their relationship with other assets. Applied Economics, 55(32), 3675–3688. https://doi.org/10.1080/00036846.2022.2117777
14. Bruzgė, R., Černevičienė, J., Šapkauskienė, A., Mačerinskienė, A., Masteika, S., & Driaunys, K. (2023). Stylized facts, volatility dynamics and risk measures of cryptocurrencies. Journal of Business Economics and Management, 24(3), 527–550. https://doi.org/10.3846/jbem.2023.19118
15. Queiroz, R. G. D. S., & David, S. A. (2024). Does anything beat a GARCH(1,1)? Evidence from crypto markets. https://doi.org/10.1007/978-3-031-69146-1_30
16. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370. https://doi.org/10.2307/2938260
17. Glosten, L. R., Jagannathan, R., & Runkle, D. (1993). On the relation between expected value and volatility. Journal of Finance, 48(5), 1779–1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
18. Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996). FIGARCH. Journal of Econometrics, 74(1), 3–30. https://doi.org/10.1016/S0304-4076(95)01749-6
19. Davidson, J. (2004). Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model. Journal of Business & Economic Statistics, 22(1), 16–29. https://doi.org/10.1198/073500103288619359
20. Naeem, M., Tiwari, A. K., Mubashra, S., & Shahbaz, M. (2019). Regime-switching GARCH for precious metals. Resources Policy, 64, 101497. https://doi.org/10.1016/j.resourpol.2019.101497
21. Khoo, T. H., Pathmanathan, D., Otto, P., & Dabo-Niang, S. (2024). A Markov-switching spatio-temporal ARCH model. Stat, 13(3), e713. https://doi.org/10.1002/sta4.713
22. Maciel, L. (2021). Cryptocurrencies VaR and ES using MSGARCH. International Journal of Finance & Economics, 26(3), 4840–4855. https://doi.org/10.1002/ijfe.2043
23. Mukhodobwane, R. M., Sigauke, C., Chagwiza, W., & Garira, W. (2020). Volatility modelling of BRICS stock markets. Statistics, Optimization & Information Computing, 8(3), 749–772. https://doi.org/10.19139/soic-2310-5070-977
24. Alqaralleh, H., Abuhommous, A. A., & Alsaraireh, A. (2020). Volatility of cryptocurrencies: GARCH-type comparison. International Journal of Financial Research, 11(4), 346–356. https://doi.org/10.5430/ijfr.v11n4p346
25. Barson, Z., & Owusu Junior, P. (2024). Tail risk modelling of cryptocurrencies. Research in Globalization, 8, Article 100229. https://doi.org/10.1016/j.resglo.2024.100229
26. Patra, S., & Gupta, N. (2025). Volume–volatility nexus with structural breaks. European Journal of Finance. https://doi.org/10.1080/1351847X.2025.2453732
27. Roy, A. (2023). EVT-based intraday risk management for cryptocurrencies. Business Perspectives and Research. https://doi.org/10.1177/22785337221148878
28. Antwi, A., Gyamfi, E. N., & Adam, A. M. (2024). Forecasting tail risk of skewed financial returns having exponential-polynomial tails. Journal of Forecasting, 43(7), 2731–2748. https://doi.org/10.1002/for.3154
29. Ryan, J. A., & Ulrich, J. M. (2024). Quantmod: R package documentation. CRAN. https://doi.org/10.32614/CRAN.PACKAGE.QUANTMOD
30. Grobys, K., & Sapkota, N. (2020). Predicting cryptocurrency defaults. Applied Economics, 52(46), 5060–5076. https://doi.org/10.1080/00036846.2020.1752903
31. Stambaugh, R. F. (2011). Inference about survivors. Quarterly Journal of Finance, 1(3), 423–464. https://doi.org/10.1142/S201013921100015
32. Tsay, R. S. (2010). Analysis of financial time series (3rd ed.). Wiley. https://doi.org/10.1002/9780470644560
33. Dickey, D. A., & Fuller, W. A. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, 74(366), 427–431. https://doi.org/10.1080/01621459.1979.10482531
34. Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303. https://doi.org/10.2307/2335207
35. Jarque, C. M., & Bera, A. K. (1987). A Test for Normality of Observations and Regression Residuals. International Statistical Review, 55(2), 163–172. https://doi.org/10.2307/1403192
36. Bai, J., & Perron, P. (2003). Multiple structural change models. Journal of Applied Econometrics, 18(1), 1–22. https://doi.org/10.1002/jae.659
37. Wilson, G. T. (2016). Book review: Time series analysis, 5th ed. Journal of Time Series Analysis, 37(5), 709–711. https://doi.org/10.1111/jtsa.12194
38. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. https://doi.org/10.1109/TAC.1974.1100705
39. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), 461–464. https://doi.org/10.1214/aos/1176344136
40. Naimy, V., Haddad, O., Fernández-Avilés, G., & El Khoury, R. (2021). Volatility of crypto and world currencies. PLOS ONE, 16(1), e0245904. https://doi.org/10.1371/journal.pone.0245904
41. Benzid, L., & Saâdaoui, F. (2024). Fractional autoregressive volatility modelling for EUR/USD. Fluctuation and Noise Letters, 23(5). https://doi.org/10.1142/S0219477524400327
42. Mighri, Z., & Jaziri, R. (2023). Long-memory and fat-tailed GARCH. Journal of Quantitative Economics, 21(1), 41–97. https://doi.org/10.1007/s40953-022-00331-w
43. Mensi, W., Al-Yahyaee, K. H., & Kang, S. H. (2019). Structural breaks and long memory in Bitcoin and ETH. Finance Research Letters, 29, 222–230. https://doi.org/10.1016/j.frl.2018.07.011
44. Faruq, U. A., Salim, D. F., & Kristanti, F. T. (2025). Risk measurement model for top-10 cryptocurrencies. Edelweiss Applied Science and Technology, 9(4), 2395–2404. https://doi.org/10.55214/25768484.v9i4.6554
45. Pečiulis, T., & Vasiliauskaitė, A. (2025). Advanced GARCH under extreme market conditions. Intellectual Economics, 19(1), 62–91. https://doi.org/10.13165/IE-25-19-1-03
46. Korkusuz, B. (2025). Volatility transmission in digital assets. Journal of Risk and Financial Management, 18(3), Article 111. https://doi.org/10.3390/jrfm18030111
47. Sun, W., & Krištoufek, L. (2024). Range-based volatility estimators outperform GARCH. Applied Economics Letters, 32(21), 3113–3120. https://doi.org/10.1080/13504851.2024.2363295
48. Queiroz, R. G. S., & David, S. A. (2023). Realized-GARCH vs GARCH for crypto volatility. Risks, 11(12), Article 211. https://doi.org/10.3390/risks11120211
49. Gao, X., Huang, W., & Wang, H. (2021). Twitter sentiment and BTC volatility. Virtual Economics, 4(1), 7–18. https://doi.org/10.34021/ve.2021.04.01(1)
50. Ciarko, M., Poszwa, G., Paluch-Dybek, A., & Timur, M. C. (2023). Cryptocurrencies as the future of money. Virtual Economics, 6(3), 70–93. https://doi.org/10.34021/ve.2023.06.03(5)
51. Shams, M., Kausar, N., & Carpentieri, B. (2025). High-order fractional iterative methods. Chaos, Solitons and Fractals, 199.
52. Sharma, P., & Vipul. (2015). Forecasting global stock index volatility. Studies in Economics and Finance, 32(4), 445–463. https://doi.org/10.1108/SEF-11-2014-0212De
53. Blasis, R. (2023). Weighted-indexed semi-Markov model. Financial Innovation, 9(1), 35. https://doi.org/10.1186/s40854-022-00418-6
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