Comparative analysis of conditional error distributions in asymmetric GARCH modelling

Abstract

This study compares the performance of GARCH-type models; GJR-GARCH (1,1), EGARCH (1,1) and APARCH (1,1) under three distinct conditional distributions: Exponentiated Student t-distribution (ESTD), Skewed Student-t distribution (SSTD), and Skewed Generalized Error Distribution (SGED) on Bitcoin data. The log returns of the Bitcoin in dollars were obtained from the daily closing prices of Bitcoin from 1^st January, 2014 to 1^st August, 2025. This time frame captures a range of market conditions, including periods of relative stability and significant shock. The data for this study was obtained from https://finance.yahoo.com website. Descriptive statistics reveal the typical financial stylized facts of heavy tails and skewness. Analysis on the data using the Augmented Dickey-Fuller (ADF) test showed stationarity and also the existence of significant ARCH effects via the ARCH-LM test. Among the asymmetric GARCH specifications estimated using Bitcoin return data, EGARCH (1,1) with exponentiated Student- t distribution (ESTD)  emerged as the best-performing error distribution.The model consistently produced the lowest Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and least forecasting values using the metrices (RMSE and MAE) relative to competing conditional error distributions, skewed student -t distributions (SSTD) and Skewed generalized error distribution (SGED). These findings suggest that the ESTD distribution provides a superior characterization of the heavy tails and asymmetry inherent in Bitcoin return volatility dynamics. The diagnostic results indicate that all volatility models adequately captured serial correlation and ARCH effects, except the GJR-GARCH(1,1)-SGED model, which exhibited significant residual autocorrelation. Overall, the EGARCH and APARCH specifications demonstrated superior model adequacy and are considered suitable for volatility forecasting.