The Fitting of Non-Stationary Time-Series Models with Time-Dependent Parameters

Abstract

Summary We use the method of weighted least squares to estimate the time-dependent parameters of non-stationary time-series models. Approximate expressions for the bias and variance of the estimates, which could be used to assess the merits of various weight functions on the basis of “mean square error” criterion, are obtained. In Section 5, it is shown that the estimates obtained by weighted least-squares method are the same as estimates obtained by weighted maximum-likelihood estimation procedure. The procedures are numerically illustrated in the last section.