Volume 26 , Issue 4 , PP: 309-326, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Alshaikh A. Shokeralla 1 *
Doi: https://doi.org/10.54216/IJNS.260427
This paper presents the Fractional Maxwell-Weibull Copula (FMWC) distribution to deal with the heavy tails, extended memory, and nonlinear dependence of price returns of Bitcoins, as the existing financial models face limitations in this aspect. The FMWC provides a flexible model that allows incorporating fractional Weibull distributions to capture persistent autocorrelation, Maxwell components to model significant price changes, and a Student-t copula to capture multivariate dependencies to discuss the volatile returns of Bitcoin. The FMWC was applied to historical Bitcoin data between January 2020 and May 2025 and showed better results than other models, such as Weibull, GARCH-t, and Maxwell-Log Logistic, with an MAE of 0.034374, RMSE of 0.0335, and log-likelihood of 4200.0. Its risk measures (VaR 95% = -0.07983, CVaR 95% = -0.10882) improve tail risk estimation, which is important in risk measurement and portfolio management. Robustness tests also validate its performance over periods and proper handling of outliers. Nevertheless, the FMWC is an excellent tool, despite its computational complexity issues, and can be used by investors, traders, and regulators. Further studies on the computational efficiencies and applications to other cryptocurrencies are required to increase their application in dynamic financial markets.
Bitcoin , Fractional Maxwell-Weibull , Long Memory , Heavy Tails , Volatility Clustering , Risk Management , Copula , Forecasting
[1] Silahli, B., Dingec, K. D., Cifter, A., and Aydin, N., “Portfolio value-at-risk with two-sided Weibull distribution: Evidence from cryptocurrency markets,” Finance Research Letters, vol. 38, p. 101425, 2021.
[2] Abdelatif, H., Ebrahim, M., Alfatemi, A., Rahouti, M., and Oliveira, D., “Cryptocurrency price forecasting using XGBoost regressor and technical indicators,” arXiv preprint, 2024.
[3] Aras, S., Özdemir, M. O., and Çılgın, C., “Uncertainty or investor attention: Which has more impact on Bitcoin volatility?,” Research in International Business and Finance, vol. 77, p. 103002, 2025.
[4] Alqaralleh, H., Al-Smadi, A. W., and Al-Khawaldeh, I., “Modelling and forecasting the volatility of cryptocurrencies: A comparison study,” Finance Research Letters, vol. 62, p. 105155, 2025.
[5] Krishna, S. J. S., Panda, A., and Sindhuja, P., “Cryptocurrency adoption and its influence on traditional financial markets,” Dynamics, vol. 8, no. 11, pp. 1–7, 2023.
[6] Catania, L., and Grassi, S., “Forecasting cryptocurrency volatility,” International Journal of Forecasting, vol. 38, no. 3, pp. 878–894, 2022.
[7] Jeleskovic, V., Latini, C., Younas, Z. I., and Al-Faryan, M. A., “Cryptocurrency portfolio optimization: Utilizing a GARCH–copula model within the Markowitz framework,” Journal of Corporate Accounting & Finance, vol. 35, no. 4, pp. 139–155, 2024.
[8] He, X., Mao, X., and Wang, Z., “Nonparametric augmented probability weighting with sparsity,” Computational Statistics & Data Analysis, vol. 191, p. 107890, 2024.
[9] Charles, A., and Darné, O., “Volatility estimation for Bitcoin: Replication and robustness,” International Economics, vol. 157, pp. 23–32, 2019.
[10] Alnami, H., Mohzary, M., Assiri, B., and Zangoti, H., “An integrated framework for cryptocurrency price forecasting and anomaly detection using machine learning,” Applied Sciences, vol. 15, p. 1864, 2025.
[11] Gupta, A. K., Sharma, S. K., and Sharma, P. K., “A novel approach for cryptocurrency price prediction using hybrid machine learning techniques,” Applied Soft Computing, vol. 119, p. 108505, 2023.
[12] Sözen, Ç., “Volatility dynamics of cryptocurrencies: A comparative analysis using GARCH-family models,” Future Business Journal, vol. 11, no. 1, p. 166, 2025.
[13] Rasekhi, M., Altun, E., Alizadeh, M., and Yousof, H. M., “The odd log-logistic Weibull-G family of distributions with regression and financial risk models,” Journal of the Operations Research Society of China, vol. 10, no. 1, pp. 133–158, 2022.
[14] Tiwari, A. K., Raheem, I. D., and Kang, S. H., “Time-varying dynamic conditional correlation between stock and cryptocurrency markets using the copula-ADCC-EGARCH model,” Physica A: Statistical Mechanics and Its Applications, vol. 535, p. 122295, 2019.
[15] Patel, N. P. et al., “Fusion in cryptocurrency price prediction: A decade survey on recent advancements, architecture, and potential future directions,” IEEE Access, vol. 10, pp. 34511–34538, 2022.
[16] Dewick, P. R., and Liu, S., “Copula modelling to analyse financial data,” Journal of Risk and Financial Management, vol. 15, no. 3, p. 104, 2022.
[17] Khatun, S., and Iqbal, M. A., “A study on modeling financial mathematics by computational program and its applications,” International Journal of Material and Mathematical Sciences, vol. 6, no. 4, pp. 100–111, 2024.
[18] Shetty, P. V., “Copula applications in cryptocurrency portfolios,” Journal of Computational Finance, vol. 27, no. 2, pp. 56–78, 2024.
[19] Taylor, S. J., and Letham, B., “Forecasting at scale,” The American Statistician, vol. 72, no. 1, pp. 37–45, 2018.
[20] Bedoui, R., Benkraiem, R., Guesmi, K., and Kedidi, I., “Portfolio optimization through hybrid deep learning and genetic algorithms vine Copula–GARCH–EVT–CVaR model,” Technological Forecasting and Social Change, vol. 197, p. 122887, 2023.
[21] Quang, P., Duy, N., Khoai, P., and Duong, B., “Integrating moving average indicators with long short-term memory model in Bitcoin price forecasting,” Journal of Applied Data Sciences, vol. 6, no. 3, pp. 1850–1864, 2025.
[22] Magris, M., Shabani, M., and Iosifidis, A., “Bayesian bilinear neural network for predicting the mid-price dynamics in limit-order book markets,” Journal of Forecasting, vol. 42, no. 6, pp. 1407–1428, 2023.
[23] Gao, Y., Zhang, Y., Lin, Z., and Jiang, A., “Bitcoin price manipulation regulation from a game perspective,” Journal of Social Computing, vol. 4, no. 4, pp. 382–397, 2023.
[24] Akter, M. S., Shahriar, H., Rahman, M. A., Rahman, M., and Cuzzocrea, A., “Early prediction of cryptocurrency price decline: A deep learning approach,” in Proc. 26th Int. Conf. Computer and Information Technology (ICCIT), 2023.
