Selecting the Appropriate Generalized Conditional Heteroscedastic Model for the Daily IMKB Index Returns

Abstract

In this study, the equitoes’ returns operated in the Istanbul Stock Exchange Market (IMKB) have been considered using the models applied for the series with high frequency. As for the data, the daily IMKB-National 100 Index has been used for the period starting from the beginning of 1988 to the mid of 2000. For this index, the most appropriate asymmetric EGARCH(2,2) model has been attained comparing different models of TGARCH, EGARCH and ARCH-M as different versions of the generalized heteroscedastic models (symmetric or asymmetric GARCH). Later on, the research has focused on whether these variables affect each other or not in the context of the Granger-causality relationship between the stock market return and the stock market return uncertainty. 1.Introduction It is accepted that the series used in the classical models for estimating time series have the same variance whereas some financial series containing high frequency and uncertainty have different variance in each period. The conditional heteroscedasticity is high in highly fluctuating periods while it is low in stagnation periods. The Autoregressive Conditional Heteroscedastic (ARCH) models related to the estimation of series high frequencies and their fluctuations changing over time have been developed first by Engle (1982). Later, Bollerslev (1986) have transferred these models by developing them into the Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. In this study, the most appropriate ARMA(p,q)-GARCH(p,q) return model is produced using the daily National-100 Index of Istanbul Stock Exchange Market (IMKB) for the period starting from the beginning of 1988 to the mid of 2000. Afterwards, the causality between the stock market return uncertainty and the real stock market return has been searched by using the Autoregressive Conditional Heteroscedasticiy of the proposed most appropriate GARCH models. In explaining the Granger-causality, we have followed the method of Grier and Perry (1998) and Nas and Perry (2000) (the later study has applied the model for the Turkish inflation) considering the relationship between inflation and inflation uncertainty.