PARAMETER-ESTIMATION FOR ARMA MODELS WITH INFINITE VARIANCE INNOVATIONS

We consider a standard ARMA process of the form phi(B)X(t) = B(B)Z(t), where the innovations Z(t) belong to the domain of attraction of a st able law, so that neither the Z(t) nor the X(t) have a finite variance . Our aim is to estimate the coefficients of phi and theta. Since maxi mum likelihood estimation is not a viable possibility (due to the unkn own form of the marginal density of the innovation sequence), we adopt the so-called Whittle estimator, based on the sample periodogram of t he X sequence. Despite the fact that the periodogram does not, a prior i, seem like a logical object to study in this non-L(2) situation, we show that our estimators are consistent, obtain their asymptotic distr ibutions and show that they converge to the true values faster than in the usual L(2) case.