Asymptotic Properties of the Wiener–Kolmogorov Predictor. Ii

Summary The asymptotic properties of the autoregressive estimates a (T)(u) obtained using the fles method (Bhansali, 1974) suggest that, in practice, a decision on truncating the a (T)(u) at u = p, say, will need to be taken. This truncated sequence of the auto-regressive estimates is used to form alternative estimates of the linear predictor, the autoregressive spectral density function and the innovation variance. Some of the asymptotic properties of these estimates are derived for the case when the observed time series is a sample of an infinite, as well as a finite, order autoregressive process. A comparison of these estimates with the corresponding estimates obtained using the time domain autoregressive coefficients is carried out.