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Semiparametric estimation by model selection for locally stationary processes

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  • Sébastien Van Bellegem
  • Rainer Dahlhaus

Abstract

Summary. Over recent decades increasingly more attention has been paid to the problem of how to fit a parametric model of time series with time‐varying parameters. A typical example is given by autoregressive models with time‐varying parameters. We propose a procedure to fit such time‐varying models to general non‐stationary processes. The estimator is a maximum Whittle likelihood estimator on sieves. The results do not assume that the observed process belongs to a specific class of time‐varying parametric models. We discuss in more detail the fitting of time‐varying AR(p) processes for which we treat the problem of the selection of the order p, and we propose an iterative algorithm for the computation of the estimator. A comparison with model selection by Akaike's information criterion is provided through simulations.

Suggested Citation

  • Sébastien Van Bellegem & Rainer Dahlhaus, 2006. "Semiparametric estimation by model selection for locally stationary processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 721-746, November.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:5:p:721-746
    DOI: 10.1111/j.1467-9868.2006.00564.x
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    Citations

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    Cited by:

    1. Dahlhaus, Rainer, 2009. "Local inference for locally stationary time series based on the empirical spectral measure," Journal of Econometrics, Elsevier, vol. 151(2), pages 101-112, August.
    2. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    3. Beran, Jan, 2007. "On parameter estimation for locally stationary long-memory processes," CoFE Discussion Papers 07/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    4. 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.
    5. Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Mélard, 2017. "Asymptotic Properties of QML Estimators for VARMA Models with Time-dependent Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 617-635, September.
    6. Eckley, Idris A. & Nason, Guy P., 2011. "LS2W: Implementing the Locally Stationary 2D Wavelet Process Approach in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i03).
    7. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," LIDAM Discussion Papers CORE 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Marios Sergides & Efstathios Paparoditis, 2009. "Frequency Domain Tests of Semiparametric Hypotheses for Locally Stationary Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 800-821, December.
    9. Cardinali Alessandro & Nason Guy P, 2011. "Costationarity of Locally Stationary Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-35, January.

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