Estimation of the index parameter for autoregressive data using the estimated innovations

In this paper we consider an invertible autoregressive process where the innovations (errors) are i.i.d. satisfying a tail regularity condition. The problem of estimation of the index of regular variation [alpha] based on a finite realization of the time series is addressed. We propose the use of a recently developed estimator of [alpha] with the data values replaced by residuals obtained from the model. Consistency and asymptotic normality of the resulting estimator are established and its performance is compared with the original estimator calculated at the data values.