On the Correlation Structure for the Generalized Autoregressive Conditional Heteroskedastic Process

Abstract. The correlation structure for the squares from the generalized autoregressive conditional heteroskedastic (GARCH) process is presented. It is shown that the behaviour of the correlations for the squares mimics the usual correlations of an appropriately defined ARMA process, although the admissible regions for the correlations are somewhat more restrictive. Simulation experiments are used to study the applicability of the theoretical results for order identification and diagnostic checking. Finally, an empirical example is given for the IBM stock market price series from Box and Jenkins (1976).