Modeling Volatility Using Bayesian GARCH with Student-t and Generalized Error Distributions: A Case Study of Bitcoin - Daniel, Adashu Jacob; Josaphat, Anule Aondolum (Darul Yasin Al Sys, 2025)
This study investigates the optimal model for capturing and forecasting volatility in the cryptocurrency market, with a specific focus on Bitcoin (BTC). Various Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models are evaluated to determine the most effective approach for modeling the stylized facts commonly observed in financial time series data. While the Maximum Likelihood Estimation (MLE) method is widely employed for estimating GARCH model parameters, this study introduces a Bayesian framework, utilizing the Metropolis-Hastings algorithm to estimate parameters of the symmetric GARCH(1,1) model. Under this approach, model parameters are treated as random variables with known prior distributions. The analysis is based on 2,000 daily BTC observations from January 2018 to June 2023, obtained from Yahoo Finance. Model selection criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Hannan–Quinn Criterion (HQC), identified the EGARCH(1,1) model under the Student-t and Generalized Error Distributions as the most suitable for capturing BTC volatility. Results further indicate the presence of volatility asymmetry and persistence, characteristic of cryptocurrency markets. In terms of predictive performance, the Bayesian GARCH(1,1) model under the Generalized Error Distribution and the EGARCH(1,1) model under the Student-t distribution exhibited the lowest values for RMSE, MAE, MAPE, and ME, confirming their suitability for future volatility forecasting in the cryptocurrency space.