Asymptotic behavior of the sample autocovariance and autocorrelation function of the AR(1) process with ARCH(1) errors

Abstract

We study the sample autocovariance and autocorrelation function of the stationary AR(1) process with ARCH(1) errors. In contrast to ARCH and GARCH processes, AR(1) processes with ARCH(1) errors can not be transformed into solutions of linear stochastic recurrence equations. However, we show that they still belong to the class of stationary sequences with regular varying finite-dimensional distributions and therefore the theory of Davis and Mikosch (1998) can be applied