Volatility Modelling in GARCH Frameworks: A Comparative Analysis of Non-Gaussian Error Distributions with Skewed Parameters.

Forecasting volatility in financial time series remains challenging due to their asymmetric nature and excess kurtosis. This study evaluates and compares the performance of four variant of GARCH models incorporating skewed non-Gaussian error innovation distribution. The performances of these GARCH family of models under the skewed error innovation distributions were evaluated for three different unique data sets to have a more robust assessment of the performance of these skewed error innovation distributions. This study leverage on daily closing prices of Bitcoin, Naira to Dollar Exchange rates and daily Nigeria All Share Index between January 1, 2015 and January 26, 2024. Model fit was assessed using Log-likelihood and Akaike Information Criterion (AIC). Forecasting accuracy was evaluated with Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE). The results confirmed the stationarity of returns and presence of ARCH effects at p < 0.05 validating the use of these volatility models. The skewed parameters in most models were significant, justifying the use of skewed innovation densities. Out-of-sample forecast showed that the skewed student-t distribution consistently outperformed other skewed innovations. Model performance varied by asset since GJR-GARCH(1,1) with Skewed Student-t was optimal for all share index based on MSE = 6.7355, RMSE = 2.5953, MAE= 1.7536. EGARCH(1,1)-sstd having MSE=1.5576, RMSE=1.2481, MAE=0.8506 for USD-Naira and GARCH(1,1)-sged with MSE=0.00009, RMSE=0.00928, MAE=0.00804 for Bitcoin. This study therefore signified the superiority of the skewed Student-t distribution in most of the cases considered. These findings offer valuable insights for investors on when and how to invest their assets.