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The Estimation Of Spectrum, Inverse Spectrum And Inverse Autocovariances Of A Stationary Time Series

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  • T. Subba Rao
  • M. M. Gabr

Abstract

. In this paper we consider the method of spectral estimation proposed by Pisarenko, and interpret its form through the properties of circular symmetric matrices. This interpretation helps us to redefine Capon's ‘high resolution’ estimation for time series defined on the real line. Using the properties of the eigenvalues and eigenvectors of Wishart matrices, we study the sampling properties of these matrices, applying a method of derivation different from that given by Pisarenko. We also show how Capon's high resolution estimator can be used to estimate the inverse spectrum and the inverse autocovariances, and we derive the asymptotic sampling properties of these estimates. The methods are illustrated with examples.

Suggested Citation

  • T. Subba Rao & M. M. Gabr, 1989. "The Estimation Of Spectrum, Inverse Spectrum And Inverse Autocovariances Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(2), pages 183-202, March.
    • Handle: RePEc:bla:jtsera:v:10:y:1989:i:2:p:183-202
    DOI: 10.1111/j.1467-9892.1989.tb00023.x
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    Cited by:

    1. R. H. Glendinning, 2000. "Estimating the Inverse Autocorrelation Function from Outlier Contaminated Data," Computational Statistics, Springer, vol. 15(4), pages 541-565, December.
    2. Caiado, Jorge & Crato, Nuno & Pena, Daniel, 2006. "A periodogram-based metric for time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2668-2684, June.
    3. Evangelos E. Ioannidis, 2022. "A new non‐parametric cross‐spectrum estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 808-827, September.

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