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Asymptotic normality of sample autocovariances with an application in frequency estimation

Author

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  • Li, Ta-Hsin
  • Kedem, Benjamin
  • Yakowitz, Sid

Abstract

The asymptotic normality of sample autocovariances is proved for time series with mixed-spectra, which extends the classical results of Bartlett for linear processes. It is also shown that the asymptotic normality remains valid after linear filtering, if the filter is strictly stable so that the end-point effect of finite sample can be ignored. The developed theory is then employed to establish the asymptotic normality of a recently proposed fast frequency estimation procedure.

Suggested Citation

  • Li, Ta-Hsin & Kedem, Benjamin & Yakowitz, Sid, 1994. "Asymptotic normality of sample autocovariances with an application in frequency estimation," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 329-349, August.
    • Handle: RePEc:eee:spapps:v:52:y:1994:i:2:p:329-349
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    Citations

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    Cited by:

    1. Kliger, Mark & Francos, Joseph M., 2007. "Asymptotic normality of the sample mean and covariances of evanescent fields in noise," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1853-1875, November.
    2. Li, Ta-Hsin, 1996. "Bartlett-type formulas for complex multivariate time series of mixed spectra," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 259-268, July.
    3. Song, Kai-Sheng & Li, Ta-Hsin, 2000. "A statistically and computationally efficient method for frequency estimation," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 29-47, March.

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