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Time Inhomogeneous Multiple Volatility Modelling

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Author Info
Wolfgang Haerdle (Humboldt Universitaet zu Berlin)
Helmut Herwartz (Humboldt Universitaet zu Berlin)
Volodia Spokoiny (Humboldt Universitaet zu Berlin)

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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 for 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 to a bivariate exchange rate series. Empirical results are compared to a parametric approach, namely the multivariate GARCH model.

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1429.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1429

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February. [Downloadable!] (restricted)
  2. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January. [Downloadable!] (restricted)
  3. Engle, Robert F & Ito, Takatoshi & Lin, Wen-Ling, 1990. "Meteor Showers or Heat Waves? Heteroskedastic Intra-daily Volatility in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 58(3), pages 525-42, May. [Downloadable!] (restricted)
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  4. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 573-92. [Downloadable!] (restricted)
  5. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  6. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August. [Downloadable!] (restricted)
  7. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  9. V. Spokoiny, . "Estimation of a Function with Discontinuities via Local Polynomial Fit with an Adaptive Window Choice," Sonderforschungsbereich 373 1998-1, Humboldt Universitaet Berlin.
  10. R. Liptser & V. Spokoiny, . "Deviation Probability Bound for Martingales with Applications to Statistical Estimation," Sonderforschungsbereich 373 1999-85, Humboldt Universitaet Berlin.
  11. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333. [Downloadable!] (restricted)
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  12. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  13. H. Herwartz, . "Structural Analysis of Portfolio Risk Using Beta Impulse Response Functions," Sonderforschungsbereich 373 1998-41, Humboldt Universitaet Berlin.
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Oliver Blaskowitz & Helmut Herwatz, . "Adaptive Forecasting of the EURIBOR Swap Term Structure," SFB 649 Discussion Papers SFB649DP2008-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. 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. [Downloadable!]
  3. Pavel Cizek & Wolfgang Härdle & Vladimir Spokoiny, 2008. "Adaptive pointwise estimation in time-inhomogeneous time-series models," SFB 649 Discussion Papers SFB649DP2008-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
    Other versions:
  4. Golosnoy, Vasyl & Herwartz, Helmut, 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. [Downloadable!]
  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. [Downloadable!]
    Other versions:
  6. 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. [Downloadable!]
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