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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 (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

Suggested Citation

  • 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
    DOI: 10.1111/1467-9892.00325
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    References listed on IDEAS

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    1. Dawei Huang, 1996. "On Low And High Frequency Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(4), pages 351-365, July.
    2. E. J. Hannan & B. G. Quinn, 1989. "The Resolution Of Closely Adjacent Spectral Lines," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(1), pages 13-31, January.
    3. An, Hong-Zhi & Chen, Zhao-Guo & Hannan, E. J., 1983. "The maximum of the periodogram," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 383-400, September.
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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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