The zero‐crossing rate of pth‐order autoregressive processes

Abstract

He and Kedem have studied the relationship between the zero‐ crossing rate (ZCR) of a second‐o rder autoregressive process and its characteristic roots and have found that, when the roots are on the unit circle, the ZCR converges in mean square to θ/π very quickly regardless of the noise level. In this paper, the ZCR of a pth‐order autoregressive process ((AR)p) is investigated. The relationships betwe en the ZCR and the one‐step asymptotic correlation function (ACF) and between the one‐step ACF and the characteristic roots of the AR(p) model are discussed, and some links between the convergence rate of the ZCR and the characte ristic roots are considered.