Limit theory for the sample covariance and correlation functions of moving averages (Q1083818)

The authors consider processes \(\{X_ t\}\) which may be represented as two-sided infinite moving averages of a sequence of i.i.d. random variates \(\{Z_ t\}\) which have regularly varying tail probabilities with index \(\alpha >0\). They derive the asymptotic distributional properties of the sample autocorrelation and autocovariance functions of \(\{X_ t\}\). In particular, in the infinite variance case \((0<\alpha <2)\), the sample autocorrelation is shown to be distributed asymptotically as the ratio of two independent stable random variables with indices \(\alpha\) /2 and \(\alpha\). Some applications to ARMA model identification and estimation using moment estimators are discussed.