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Zbl 0674.62057
Mackisack, M.S.; Poskitt, D.S.
Autoregressive frequency estimation. (English)
[J] Biometrika 76, No.3, 565-575 (1989). ISSN 0006-3444; ISSN 1464-3510/e

Summary: Presume that an autoregressive model of given order is fitted to data obtained from a realization of a sinusoidal signal embedded in white noise. This paper investigates the statistical properties of the estimate of the frequency of the signal obtained by minimizing the transfer function of the autoregression. \par Strong consistency and convergence in distribution of the estimate are established when the order of the autoregression is allowed to increase with sample size at an appropriate rate. It is also shown that the operational characteristics of commonly-used order determination procedures are such as to produce values of the selected order compatible with the application of the asymptotic theory. The outcome of some simulation experiments and an empirical example illustrating the practical impact of the results obtained are also presented.

MSC 2000:: *62M10 Time series, etc. (statistics)
62M09 Non-Markovian processes: estimation
62M15 Spectral analysis of processes

Keywords: asymptotic normality; discrete spectra; autoregressive model; sinusoidal signal; white noise; frequency; minimizing the transfer function of the autoregression; Strong consistency; convergence in distribution; order determination; simulation experiments

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