Analyzing the Performance of Symmetrical and Asymmetrical GARCH Models and Presentation of the Optimal Model in Predicting Price Index Fluctuations and Cash Return of Tehran Stock Exchange

Abstract

This study aims to present an optimal model for modeling the volatility of the Tehran Stock Exchange Price and Dividend Index during the period 2013 to 2024. It investigates the factors contributing to the superiority of GARCH models and seeks to determine whether certain models systematically outperform others, and under what conditions such superiority occurs. To this end, an evolutionary process based on the conventional steps of identification, estimation, and diagnostic testing, as outlined in the Box-Jenkins methodology, was employed. To evaluate model performance, a set of criteria was utilized, including log-likelihood, three information criteria, the Mincer-Zarnowitz time series test, and various loss functions for assessing both in-sample and out-of-sample performance. The findings of the study indicate that market conditions (periods of stability or crisis) significantly affect the performance of GARCH models. During crisis periods, asymmetric GARCH models demonstrate superior performance in forecasting market volatility and are considered more suitable. In contrast, under stable market conditions, the simple GARCH model, with its adequate efficiency and lower cost, is deemed a more economical choice. Furthermore, the results suggest that incorporating external variables and employing nonlinear models improves the quality of modeling in crisis situations. This improvement is evident not only in the accuracy of in-sample estimates but also in the out-of-sample forecasting power. Although in times of crisis the implied volatility index provides more information than the standard GARCH model, using heavy-tailed distributions such as the Student’s t-distribution does not lead to a significant improvement in model performance compared to the normal distribution. Therefore, based on the results of this study, it can be concluded that the standard GARCH model is an efficient choice during stable periods. However, during crisis conditions, the GJR asymmetric GARCH model especially when augmented with external variables can be considered an optimal model for estimating and forecasting the volatility of the Tehran Stock Exchange Price and Dividend Index.