An Analysis of the Predictive Ability of ARIMA-GARCH Models on the S&P 500 Index During the 2008 Financial Crisis and the 2020 COVID-19 Pandemic

With the increasing volatility of global financial markets, effectively predicting market trends and managing potential risks has become an important issue in financial risk management and investment decisions. This paper evaluates the forecasting ability of the ARIMA-GARCH model for the logarithmic return of the S&P 500 index during the 2008 economic crisis and the 2020 COVID-19 pandemic. It assesses the VaR forecasting performance of the model, mainly using rolling window forecasting combined with the Kupiec test and the Christoffersen test. Given that the 2008 financial crisis originated from internal risks in the financial system, while the economic shock triggered by the COVID-19 pandemic in 2020 was an external event impacting the financial system, the model’s forecast performance differs between the two periods. The test results show that the ARIMA-GARCH model has little predictive power for the S&P 500 index during the 2008 economic crisis, while during COVID-19, its predictive power is significantly dependent on the model’s distribution assumptions and the confidence level settings. In particular, we find that the model can predict market risk more accurately under the GED distribution assumption during COVID-19. This suggests the need for flexible model adjustments under extreme market conditions depending on the actual situation. The research results provide a reference for the application conditions of the ARIMA-GARCH model in the financial market and provide directions for model improvement.