Autoregressive frequency estimation

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. 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.

[1]  A. M. Walker,et al.  A Survey of statistical work on the Mackenzie River series of annual Canadian lynx trappings for the , 1977 .

[2]  T. Anderson.  Statistical analysis of time series , 1974 .

[3]  A. M. Walker.  On the estimation of a harmonic component in a time series with stationary independent residuals , 1971 .

[4]  R. Kumaresan,et al.  Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood , 1982, Proceedings of the IEEE.

[5]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[6]  Petre Stoica,et al.  Asymptotic bias of the high-order autoregressive estimates of sinusoidal frequencies , 1987 .

[7]  B. Friedlander.  Lattice methods for spectral estimation , 1982, Proceedings of the IEEE.

[8]  E. J. Hannan,et al.  Non-linear time series regression , 1971, Journal of Applied Probability.

[9]  M. S. Mackisack,et al.  SOME PROPERTIES OF AUTOREGRESSIVE ESTIMATES FOR PROCESSES WITH MIXED SPECTRA , 1990 .

[10]  S. Lawrence Marple.  Spectral line analysis by Pisarenko and Prony methods , 1979, ICASSP.

[11]  E. J. Hannan,et al.  The estimation of frequency , 1973, Journal of Applied Probability.

[12]  L. Marple.  A new autoregressive spectrum analysis algorithm , 1980 .

[13]  M. Priestley,et al.  A Study of Autoregressive and Window Spectral Estimation , 1981 .

[14]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[15]  John A. Rice,et al.  On frequency estimation , 1988 .

[16]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[17]  S.M. Kay,et al.  Spectrum analysis—A modern perspective , 1981, Proceedings of the IEEE.

[18]  Howell Tong.  Some comments on the Canadian Lynx data with discussion , 1977 .