Investigation of Some Heteroscedastic Models on Volatility Return under some Skewed-Distributed Error Innovations

This study explores the performance of various heteroscedastic models in modeling and forecasting the volatility of financial returns, incorporating skewed-distributed error innovations to address the asymmetry and heavy tails observed in financial data. Volatility modeling is pivotal in financial econometrics, where understanding the variability of returns is essential for risk management, option pricing, and investment strategies. The investigation focuses on models from the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) family, including standard GARCH, Exponential GARCH (EGARCH), and Threshold GARCH (TGARCH), extended to accommodate skewed error distributions such as the Skewed Normal (SN), Skewed Student-t (SSt), and Skewed Generalized Error Distribution (SGED). Using empirical financial time series data, the models are compared based on their ability to capture volatility clustering, leverage effects, and asymmetric distributional properties of returns. Estimation of the models is performed through maximum likelihood techniques, and their performance is evaluated using criteria such as Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and out-of-sample forecast accuracy. The results demonstrate that incorporating skewed-distributed error innovations significantly enhances the models' ability to capture the statistical properties of financial returns, leading to improved volatility forecasts. The findings highlight the importance of using skewed distributions in financial volatility modeling, providing more accurate tools for practitioners in risk assessment and financial decision-making. This study contributes to the ongoing development of more robust and flexible econometric models for financial markets.