Application of Least Squares to the Search for Periodicities

Abstract

Recalling that the method of estimation by generalized least squares enables testing of hypotheses on the parameters under estimation, advantage is taken from the fact that the solution given by the classical harmonic analysis is identical with the one given by least squares to select those components significantly different from zero. The necessary levels of significance are found through a generalization of Walker's criterion. The same idea is applied to the search for periodicities in time series. In this case, special properties of the series of sample autocovariances and of autoregressive series are used as auxiliary tools. The illustrations given concern the estimation of daily normals of the mean outdoor temperature at Uccle (Brussels) and the establishment that the sunspot activity is an essentially periodic phenomenon. Errors of estimation are computed in both cases.