Limit theorems for the sample autocovariance of a continuous-time moving average process with long memory

Abstract

We examine the asymptotic behaviour of the sample autocovariance in a continuous-time moving average model with long-range dependence. We show that it is either asymptotically Rosenblatt distributed or stable distributed. This shows that results by Horv\'ath and Kokoszka for discrete-time moving average processes with long memory also hold for continuous-time moving average processes.