Research on the volatility forecasting model of KOSPI index returns using AR(M)-GARCH(P,Q) model

Abstract

In this study, we estimated the volatility of the KOSPI index returns and analyzed volatility trends. The data used in the study consisted of monthly observations from January 2005 to December 2022, and the KOSPI index raw data was transformed into log returns. The volatility estimation model used the AR(m)-GARCH(p,q) model, which combines the autoregressive error model and the GARCH model that explains the persistence of volatility at low orders. The goodness of fit of the model was confirmed using the Portmanteau Q-test and LM-test. Applying the autoregressive error model revealed significant autocorrelation in the log returns of the KOSPI index at lags 3 and 6. Residual analysis indicated that the residuals followed white noise, but the squared residuals exhibited heteroscedasticity. Therefore, after fitting the autoregressive error model, we applied the GARCH model and conducted residual analysis, finding both the residuals and squared residuals significant at a 5% significance level. The volatility forecasting results indicated a continuous increase in volatility. The findings of this study are expected to provide important implications for policymakers responsible for risk management in the Korean stock market.