Autoregressive and window estimates of the inverse correlation function

Abstract

The concept of the inverse correlation function of a stationary process x t was first introduced by Cleveland (1972), who also introduced the autoregressive and the window methods for estimating this function. The asymptotic distribution of the estimates provided by these two methods is derived and their asymptotic covariance structure is shown to be in accordance with a remark of Parzen (1974). The results are extended to show that the two procedures suggested by Durbin (1959, 1961) for estimating the parameters of a moving average model are asymptotically efficient, relative to maximum likelihood in the Gaussian case.