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Nonstationary Yule-Walker equations

Author

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  • Hallin, Marc
  • Ingenbleek, Jean-François

Abstract

A nonstationary generalization of the classical Yule-Walker equations, relating the (time-varying) autocorrelations of an autoregressive process to the coefficients of the possible models for this process, is given. The corresponding theoretical model-building (or spectral factorization) problem, i.e., that of expressing the above mentioned models in terms of the autocorrelations, is solved. This paper, as well as several others, is part of a work whose purpose is a systematic study of time-varying ARMA models.

Suggested Citation

  • Hallin, Marc & Ingenbleek, Jean-François, 1983. "Nonstationary Yule-Walker equations," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 189-195, June.
    • Handle: RePEc:eee:stapro:v:1:y:1983:i:4:p:189-195
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    Cited by:

    1. Abdelkamel Alj & Christophe Ley & Guy Melard, 2015. "Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients: Part I," Working Papers ECARES ECARES 2015-21, ULB -- Universite Libre de Bruxelles.
    2. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    3. M. Shelton Peiris & Manabu Asai, 2016. "Generalized Fractional Processes with Long Memory and Time Dependent Volatility Revisited," Econometrics, MDPI, vol. 4(3), pages 1-21, September.

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