Sample correlation behavior for the heavy tailed general bilinear process

Abstract

In this paper, we consider the class of general bilinear models given by , where is an i.i.d. sequence of heavy tailed noise variables, and where . By means of a point process analysis, we show that the sample correlation function converges in distribution to a nondegenerate random variable. Thus standard model selection and fitting tools when applied to nonlinear heavy tailed models will be misleading. Also, consistency of the Hill estimator as an estimate of the tail index for this class of bilinear models is proved