A Model for Estimating Stock Market Shocks Using the ARMA-GARCH Approach

Ebrahim  Rahimi; Ahmad Mohammadi; Ali Asghar  Motaghi; Seyyed Ali  Paytakhti Oskooe

doi:10.61838/kman.ijimob.3.5.21

Authors

Ebrahim Rahimi PhD Student, Department of Financial Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran

Ahmad Mohammadi * Assistant Professor of Accounting Department, Tabriz Branch, Islamic Azad University, Tabriz, Iran iacp_a-mohammadi@yahoo.com

Ali Asghar Motaghi Assistant Professor of Accounting Department, Tabriz Branch, Islamic Azad University, Tabriz, Iran

Seyyed Ali Paytakhti Oskooe Associate Professor, Department of Economics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

https://doi.org/10.61838/kman.ijimob.3.5.21

Keywords:

Time series, Market shock, ARMA model, GARCH model

Abstract

Objective: Linear ARMA and GARCH models have numerous applications in the field of time series forecasting. The primary objective of this article is to present a model for estimating stock market shocks based on the ARMA-GARCH model in the Tehran Stock Exchange.

Methodology: For this purpose, 15-minute intraday data of the overall index and the equal-weighted index for the period from June 10, 2018, to March 18, 2019, including the opening, closing, highest, and lowest values of the mentioned indices, were used. For the analysis and fitting of the models to estimate market shocks, the Pandas, Numpy, and armagarch packages in Python 3.9 software were employed. The goodness-of-fit test was used to evaluate the suitability of the fitted models.

Findings: The results indicated that the fitted models for estimating market shocks, based on the Akaike criterion and the goodness-of-fit test, were the best and most suitable models, although the selected models differed for the two indices.

Conclusion: The findings of this study indicate that the ARMA-GARCH model is effective in estimating stock market shocks in the Tehran Stock Exchange. The optimal models identified were ARMA(2,3)-GARCH(1,1) for the overall index and ARMA(1,2)-GARCH(1,1) for the equal-weighted index. The results suggest that while the ARMA order varied between the indices, the GARCH order remained consistent, highlighting the model's robustness. Additionally, the analysis demonstrated that the new series of changes (market shocks) were completely random and non-normal, confirming the model's capability in accurately capturing market dynamics and providing valuable insights for traders and policymakers.