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Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models

Author

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  • P. Čížek
  • W. Härdle
  • V. Spokoiny

Abstract

This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general, local parametric approach particularly applies to general varying-coefficient parametric models, such as GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition and change-point 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. Copyright © 2009 The Author(s). Journal compilation © Royal Economic Society 2009

Suggested Citation

  • P. Čížek & W. Härdle & V. Spokoiny, 2009. "Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 248-271, July.
    • Handle: RePEc:ect:emjrnl:v:12:y:2009:i:2:p:248-271
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    Cited by:

    1. Meister, Alexander & Kreiß, Jens-Peter, 2016. "Statistical inference for nonparametric GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3009-3040.
    2. Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl & Klochkov, Yegor, 2019. "SONIC: SOcial Network with Influencers and Communities," IRTG 1792 Discussion Papers 2019-025, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. 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.
    4. Xiu Xu & Andrija Mihoci & Wolfgang Karl Hardle, 2020. "lCARE -- localizing Conditional AutoRegressive Expectiles," Papers 2009.13215, arXiv.org.
    5. Wolfgang K. Härdle & Nikolaus Hautsch & Andrija Mihoci, 2015. "Local Adaptive Multiplicative Error Models for High‐Frequency Forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 529-550, June.
    6. Bruno Spilak & Wolfgang Karl Hardle, 2020. "Tail-risk protection: Machine Learning meets modern Econometrics," Papers 2010.03315, arXiv.org, revised Aug 2021.
    7. Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl & Klochkov, Yegor, 2022. "SONIC: SOcial Network analysis with Influencers and Communities," Journal of Econometrics, Elsevier, vol. 228(2), pages 177-220.
    8. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," LIDAM Discussion Papers CORE 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Niels Gillmann & Ostap Okhrin, 2023. "Adaptive local VAR for dynamic economic policy uncertainty spillover," Papers 2302.02808, arXiv.org.
    10. Matthias R. Fengler & Ostap Okhrin, 2012. "Realized Copula," SFB 649 Discussion Papers SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Cizek, P., 2010. "Modelling Conditional Heteroscedasticity in Nonstationary Series," Other publications TiSEM a5a7b05f-5f1f-46ed-8ce8-5, Tilburg University, School of Economics and Management.
    12. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    13. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2018. "lCARE - localizing conditional autoregressive expectiles," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 198-220.
    14. Härdle Wolfgang Karl & Okhrin Ostap & Okhrin Yarema, 2013. "Dynamic structured copula models," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 361-388, December.
    15. 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.
    16. Wolfgang Karl Härdle & Andrija Mihoci & Christopher Hian-Ann Ting, 2014. "Adaptive Order Flow Forecasting with Multiplicative Error Models," SFB 649 Discussion Papers SFB649DP2014-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    17. Chen, C. Y-H. & Härdle, W. K. & Klochkov, Y., 2019. "Influencers and Communities in Social Networks," Cambridge Working Papers in Economics 1998, Faculty of Economics, University of Cambridge.
    18. Andrija Mihoci & Christopher Hian-Ann Ting & Meng-Jou Lu & Kainat Khowaja, 2022. "Adaptive order flow forecasting with multiplicative error models," Digital Finance, Springer, vol. 4(1), pages 89-108, March.
    19. Shen, Zhiwei, 2016. "Adaptive local parametric estimation of crop yields: implication for crop insurance ratemaking," 156th Seminar, October 4, 2016, Wageningen, The Netherlands 249984, European Association of Agricultural Economists.
    20. Dedy Dwi Prastyo & Wolfgang Karl Härdle, 2014. "Localising Forward Intensities for Multiperiod Corporate Default," SFB 649 Discussion Papers SFB649DP2014-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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