On the Relation Between Fitting Autoregression and Periodogram with Applications

Abstract

The relation between fitting autoregression and periodogram is herein presented. More specifically, the asymptotic error covariance matrices of the estimates of the autoregressive parameters using Yule-Walker equations are expressed in terms of the periodogram. These expressions permit the immediate calculation of the error covariance matrices for various time series problems including the autoregressive spectral estimation and fitting autoregression to the data with randomly missed observations.