An Optimality Property of the Least-Squares Estimate of the Parameter of the Spectrum of a Purely Nondeterministic Time Series

Abstract

Whittle has proved that the least-squares estimator of a scalar parameter of the spectrum of a purely nondeterministic time series possesses a certain optimality property independently of the distribution of the residuals. In this paper we furnish a proof in full detail of the corresponding result for a vector parameter and also provide some examples which illustrate the application of the result.