A note on estimation by least squares for harmonic component models

A. M. Walker

Journal of Time Series Analysis, 2003, vol. 24, issue 5, 613-629

Abstract: Abstract. Let observations (X1,…,Xn) be generated by a harmonic model such that Xt=A0 cos ω0t+B0 sin ω0t+εt, where A0,B0,ω0 are constants and (εt) is a stationary process with zero mean and finite variance. The estimation of A0,B0,ω0 by the method of least squares is considered. It is shown that, without any restriction on ω in the minimization procedure, the estimate is an n‐consistent estimate of ω0, and hence () has the usual asymptotic distribution. The extension to a harmonic model with k>1 components is discussed. The case k=2 is considered in detail, but it was only found possible to establish the result under the restriction that both angular frequencies lie in the interval

Date: 2003
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