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A note on estimation by least squares for harmonic component models

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  • A. M. Walker

Abstract

Let observations (X_1, H ,X_n) be generated by a harmonic model such that X_t=A_0 cos omega_0t + B_0 sin omega_0t + epsilon _t, where A_0,B_0, omega_0 are constants and ( epsilon _t) is a stationary process with zero mean and finite variance. The estimation of A_0,B_0, omega_0 by the method of least squares is considered. It is shown that, without any restriction on omega in the minimization procedure, the estimate is an n-consistent estimate of omega_0, and hence ( ) has the usual asymptotic distribution. Copyright 2003 Blackwell Publishing Ltd.

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  • A. M. Walker, 2003. "A note on estimation by least squares for harmonic component models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 613-629, September.
  • Handle: RePEc:bla:jtsera:v:24:y:2003:i:5:p:613-629
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    Cited by:

    1. Miguel Artiach, 2011. "Second-order moments of frequency asymmetric cycles," Working Papers. Serie AD 2011-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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