SOME PROPERTIES OF THE LEAST SQUARES ESTIMATOR OF THE PARAMETERS OF THE HIDDEN PERIODICTY MODEL

Abstract

A stochastic process consisting of k>1 harmonic components plus stationary errors is considered under two models, models I and II for uni- and bi- directional data respectively. The asymptotic joint distribution of the frequencies and other parameters of the models are proved under both models as a direct consequence of the basic consistency of the frequencies as opposed to the proof given in Walker [6] for the approximate least squares estimator of the parameters of model I. Also the problems encountered by Walker [6] Section 5 when dealing with k>1 frequencies are overcome.