Muneer, S., Leal, C. C., & Oliveira, B. (2025). Analyzing Volatility Patterns of Bitcoin Using the GARCH Family Models. Operations Research Forum, 6(2). https://doi.org/10.1007/s43069-025-00482-5

This paper analyzes and forecasts Bitcoin volatility using the GARCH family of models. Bitcoin, known for its speculative nature and high volatility compared to gold, exhibits volatility persistence and long memory, justifying the use of GARCH models. The study employs daily closing prices from July 18, 2015, to September 4, 2023, totaling 2,970 observations. Six AR(1)-GARCH-type models were tested under a Gaussian distribution, with data divided into in-sample and out-of-sample periods. The AR(1)-ACGARCH(1,1) model provided the best fit according to log-likelihood, AIC, SIC, and HQ criteria, highlighting significant volatility persistence and a negative leverage effect. For volatility forecasting, the AR(1)-PGARCH(1,1) model achieved the best predictive performance, minimizing MAE, Theil, and MAPE errors. Results suggest that asymmetric models capture Bitcoin’s volatility dynamics more accurately. The findings emphasize Bitcoin’s relevance for portfolio and risk management and recommend future research using non-Gaussian distributions, such as the t-distribution, to enhance predictive accuracy.