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Nonstationary Yule-Walker equations

Author

Listed:
  • Marc Hallin
  • Jean-François Ingenbleek

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. © 1983.

Suggested Citation

  • Marc Hallin & Jean-François Ingenbleek, 1983. "Nonstationary Yule-Walker equations," ULB Institutional Repository 2013/1999, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/1999
    Note: SCOPUS: ar.j
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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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