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An explicit representation of Verblunsky coefficients

Author

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  • Bingham, N.H.
  • Inoue, Akihiko
  • Kasahara, Yukio

Abstract

We prove a representation of the partial autocorrelation function (PACF) of a stationary process, or of the Verblunsky coefficients of its normalized spectral measure, in terms of the Fourier coefficients of the phase function. It is not of fractional form, whence simpler than the existing one obtained by the second author. We apply it to show a general estimate on the Verblunsky coefficients for short-memory processes as well as the precise asymptotic behavior, with remainder term, of those for FARIMA processes.

Suggested Citation

  • Bingham, N.H. & Inoue, Akihiko & Kasahara, Yukio, 2012. "An explicit representation of Verblunsky coefficients," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 403-410.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:403-410
    DOI: 10.1016/j.spl.2011.11.004
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    References listed on IDEAS

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    1. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
    2. Inoue, Akihiko & Kasahara, Yukio, 2004. "Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 135-147, April.
    3. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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    Cited by:

    1. Takemura, Akimichi, 2016. "Exponential decay rate of partial autocorrelation coefficients of ARMA and short-memory processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 207-210.

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