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Adaptive pointwise estimation in time-inhomogeneous time-series models

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  • Čížek, Pavel
  • Härdle, Wolfgang Karl
  • Spokoiny, Vladimir

Abstract

This paper offers a new method for estimation and forecasting of the linear and nonlinear time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as AR or GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition, and changepoint models are special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right-end point by a local change-point analysis. We construct locally adaptive estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. In the particular case of GARCH estimation, the proposed method is applied to stock-index series and is shown to outperform the standard parametric GARCH model.

Suggested Citation

  • Čížek, Pavel & Härdle, Wolfgang Karl & Spokoiny, Vladimir, 2008. "Adaptive pointwise estimation in time-inhomogeneous time-series models," SFB 649 Discussion Papers 2008-002, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2008-002
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    Cited by:

    1. Schroeder, Anna Louise & Fryzlewicz, Piotr, 2013. "Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery," LSE Research Online Documents on Economics 54934, London School of Economics and Political Science, LSE Library.
    2. Bruno Spilak & Wolfgang Karl Hardle, 2020. "Tail-risk protection: Machine Learning meets modern Econometrics," Papers 2010.03315, arXiv.org, revised Aug 2021.
    3. Giammarino, Flavia & Barrieu, Pauline, 2009. "A semiparametric model for the systematic factors of portfolio credit risk premia," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 655-670, September.
    4. Fengler, Matthias R. & Okhrin, Ostap, 2012. "Realized copula," SFB 649 Discussion Papers 2012-034, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Bruno Spilak & Wolfgang Karl Härdle, 2022. "Tail-Risk Protection: Machine Learning Meets Modern Econometrics," Springer Books, in: Cheng-Few Lee & Alice C. Lee (ed.), Encyclopedia of Finance, edition 0, chapter 92, pages 2177-2211, Springer.

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    More about this item

    Keywords

    adaptive pointwise estimation; autoregressive models; conditional heteroscedasticity models; local time-homogeneity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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