Exponentiated student-t distribution: properties and modelling of financial data using asymmetric GARCH models

Abstract

This study proposes a novel error innovation, the Exponentiated Student-t Distribution (ESTD), to enhance volatility modeling within asymmetric GARCH frameworks. The performance of the proposed innovation is evaluated against conventional distributions—Student-t and Generalized Error Distribution (GED)—using both simulated data and empirical returns from the S&P 500 index. Two asymmetric GARCH models, EGARCH (1,1) and GJR-GARCH (1,1), are employed to capture volatility dynamics, including leverage effects. Model evaluation considers both in-sample fit (log-likelihood, AIC, BIC) and out-of-sample forecasting accuracy (MSE, RMSE, MAE). Results consistently indicate that models incorporating ESTD outperform the benchmarks across both model specifications, yielding higher log-likelihood values, lower information criteria, and reduced forecast errors. The persistence measures under the ESTD specification remain below unity and are comparable to those obtained under GED and Student-t assumptions The GJR-GARCH (1,1) model with ESTD exhibits the strongest overall performance, effectively capturing asymmetric volatility responses and extreme market fluctuations. Economically, the ESTD innovation improves the representation of fat tails and extreme shocks, providing more reliable volatility forecasts for financial risk management, derivative pricing, and portfolio allocation. The findings demonstrate the practical advantages of the ESTD distribution over conventional innovations, highlighting its contribution to the literature on volatility modeling. This study therefore contributes to the growing literature on flexible innovation distributions in GARCH-type models by introducing an exponentiated heavy-tailed specification that improves the modeling of extreme financial returns without substantially increasing estimation complexity.