On the asymptotic behaviour of the sample autocovariance function for an integrated moving average process

Abstract

SUMMARY In this paper, we derive the first two asymptotic moments of the autooovariance function of a time series generated from an integrated moving average process of order (1,1). In particular, it is found that the expected value of the sample autocovariance at lag k is approximately proportional to the length of the series. This result suggests a method of checking whether a nonstationary time series can be described by an integrated moving average process of order (1,1) and its use is illustrated with a simulated series.