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Time inhomogeneous multiple volatility modelling

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  • Härdle, Wolfgang
  • Herwartz, Helmut
  • Spokoiny, Vladimir G.

Abstract

Price variations observed at speculative markets exhibit positive autocorrelation and cross correlation among a set of assets, stock market indices, exchange rates etc. A particular problem in investigating multivariate volatility processes arises from the high dimensionality implied by a simultaneous analysis of variances and covariances. Parametric volatility models as e.g. the multivariate version of the prominent GARCH model become easily intractable für empirical work. We propose an adaptive procedure that aims to identify periods of second order homogeneity for each moment in time. Similar to principal component analysis the dimensionality problem is solved by transforming a multivariate series into a set of univariate processes. We discuss thoroughly implementation issues which naturally arise in the framework of adaptive modelling. Theoretical and Monte Carlo results are given. The empirical performance of the new method is illustrated by an application 1,0 a bivariate exchange rate series and a 23-dimensional system of asset returns. Empirical results of the FX~analysis are compared to a parametric approach, namely the multivariate GARCH model.

Suggested Citation

  • Härdle, Wolfgang & Herwartz, Helmut & Spokoiny, Vladimir G., 2001. "Time inhomogeneous multiple volatility modelling," SFB 373 Discussion Papers 2001,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:20017
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    Cited by:

    1. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    2. Oliver Blaskowitz & Helmut Herwartz, 2009. "Adaptive forecasting of the EURIBOR swap term structure," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(7), pages 575-594.
    3. Mazur Błażej & Pipień Mateusz, 2018. "Time-varying asymmetry and tail thickness in long series of daily financial returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-21, December.
    4. Herwartz, Helmut & Golosnoy, Vasyl, 2007. "Semiparametric Approaches to the Prediction of Conditional Correlation Matrices in Finance," Economics Working Papers 2007-23, Christian-Albrechts-University of Kiel, Department of Economics.
    5. Oliver Blaskowitz & Helmut Herwartz & Gonzalo de Cadenas Santiago, 2005. "Modeling the FIBOR/EURIBOR Swap Term Structure: An Empirical Approach," SFB 649 Discussion Papers SFB649DP2005-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. C. Stéphan & S. Skander, 2003. "Statistical analysis of financial time series under the assuption of local stationarity," THEMA Working Papers 2003-23, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. 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.
    8. Cizek, P. & Haerdle, W. & Spokoiny, V., 2007. "Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models," Other publications TiSEM a797e4a8-12cf-4ac5-9fae-b, Tilburg University, School of Economics and Management.
    9. Enzo Giacomini & Wolfgang Härdle, 2005. "Value-at-Risk Calculations with Time Varying Copulae," SFB 649 Discussion Papers SFB649DP2005-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Chaohua Dong & Jiti Gao, 2011. "Expansion of Brownian Motion Functionals and Its Application in Econometric Estimation," Monash Econometrics and Business Statistics Working Papers 19/11, Monash University, Department of Econometrics and Business Statistics.
    11. Bruno Spilak & Wolfgang Karl Hardle, 2020. "Tail-risk protection: Machine Learning meets modern Econometrics," Papers 2010.03315, arXiv.org, revised Aug 2021.
    12. Golosnoy, Vasyl & Ragulin, Sergiy & Schmid, Wolfgang, 2011. "CUSUM control charts for monitoring optimal portfolio weights," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2991-3009, November.
    13. Cizek, P., 2010. "Modelling Conditional Heteroscedasticity in Nonstationary Series," Discussion Paper 2010-84, Tilburg University, Center for Economic Research.
    14. Härdle, Wolfgang Karl & Chen, Ying & Schulz, Rainer, 2004. "Prognose mit nichtparametrischen Verfahren," Papers 2004,07, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    15. Jianqing Fan & Yingying Fan & Jinchi Lv, 0. "Aggregation of Nonparametric Estimators for Volatility Matrix," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 321-357.
    16. Golosnoy, Vasyl & Schmid, Wolfgang & Seifert, Miriam Isabel & Lazariv, Taras, 2020. "Statistical inferences for realized portfolio weights," Econometrics and Statistics, Elsevier, vol. 14(C), pages 49-62.
    17. Błażej Mazur & Mateusz Pipień, 2012. "On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(2), pages 95-116, June.
    18. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," LIDAM Discussion Papers CORE 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Golosnoy, Vasyl & Okhrin, Yarema, 2009. "Flexible shrinkage in portfolio selection," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 317-328, February.
    20. Chen, Ying & Härdle, Wolfgang & Spokoiny, Vladimir, 2010. "GHICA -- Risk analysis with GH distributions and independent components," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 255-269, March.

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    Keywords

    stochastic volatility model; adaptive estimation; local homogeneity;
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