More limit theory for the sample correlation function of moving averages (Q1062404)

Let \(X_ t=\sum^{\infty}_{j=-\infty}c_ jZ_{t-j}\) be a linear process where \(Z_ t\) are i.i.d. random variables, the distribution of which belongs to the domain of attraction of a stable law with index \(\alpha\in (0,2]\). If \(E| Z_ 1|^{\alpha}<\infty\) and \(\alpha\in (0,2)\), then under some general conditions the normalized sample correlation function of \(\{X_ t\}\) converges in distribution to the ratio of two dependent stable random variables with indices \(\alpha\) and \(\alpha\) /2. This differs markedly from the case when \(E| Z_ 1|^{\alpha}=\infty\), because the same authors proved in earlier papers that then the limit distribution corresponds to the ratio of two independent stable variables.