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Biometrika 1989 76(3):565-575; doi:10.1093/biomet/76.3.565
© 1989 by Biometrika Trust
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Autoregressive frequency estimation

M. S. MACKISACK and D. S. POSKITT

Department of Statistics, I.A.S., Australian National University Canberra, A.C.T. 2601, Australia

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. 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.

Key Words: Asymptotic normality • Autoregression • Consistency • Discrete spectra • Frequency • Noise • Order selection • Signal


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