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Time inhomogeneous multiple volatility modelling

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Author Info

  • 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. --

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Bibliographic Info

Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2001,7.

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Date of creation: 2001
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Handle: RePEc:zbw:sfb373:20017

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Keywords: stochastic volatility model; adaptive estimation; local homogeneity;

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References

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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. Liptser, R. & Spokoiny, Vladimir G., 1999. "Deviation probability bound for martingales with applications to statistical estimation," SFB 373 Discussion Papers 1999,85, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  4. Robert F. Engle & Takatoshi Ito & Wen-Ling Lin, 1991. "Meteor Showers or Heat Waves? Heteroskedastic Intra-Daily Volatility in the Foreign Exchange Market," NBER Working Papers 2609, National Bureau of Economic Research, Inc.
  5. 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.
  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.
  7. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  8. 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.
  9. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  10. repec:wop:humbsf:1998-41 is not listed on IDEAS
  11. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
  12. H. Herwartz, 1998. "Structural Analysis of Portfolio Risk Using Beta Impulse Response Functions," SFB 373 Discussion Papers 1998,41, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  13. repec:wop:humbsf:1999-85 is not listed on IDEAS
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Citations

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Cited by:
  1. 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.
  2. Härdle, Wolfgang Karl & Chen, Ying & Schulz, Rainer, 2004. "Prognose mit nichtparametrischen Verfahren," Papers 2004,07, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  3. Oliver Blaskowitz & Helmut Herwatz, 2008. "Adaptive Forecasting of the EURIBOR Swap Term Structure," SFB 649 Discussion Papers SFB649DP2008-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Yuanhua Feng & David Hand & Keming Yu, 2012. "A Multivariate Random Walk Model with Slowly Changing Drift and Cross-correlation Applied to Finance," Working Papers 50, University of Paderborn, CIE Center for International Economics.
  5. 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.
  6. 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.
  7. Blaskowitz, Oliver J. & Herwartz, Helmut & de Cadenas Santiago, Gonzalo, 2005. "Modeling the FIBOR/EURIBOR Swap Term Structure : An Empirical Approach," Economics Working Papers 2005,04, Christian-Albrechts-University of Kiel, Department of Economics.
  8. 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.
  9. 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, CEJEME, vol. 4(2), pages 95-116, June.
  10. Jianqing Fan & Yingying Fan & Jinchi Lv, 0. "Aggregation of Nonparametric Estimators for Volatility Matrix," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(3), pages 321-357.
  11. 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.

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