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Flexible multivariate GARCH modeling with an application to international stock markets

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  • Olivier Ledoit
  • Pedro Santa Clara
  • Michael Wolf

Abstract

The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk measurement, portfolio selection, and tests of asset pricing models, this is a very important problem in practice. Our model of choice is the Diagonal-Vech version of the Multivariate GARCH(1,1) model. The problem is that the estimation of the general Diagonal-Vech model model is numerically infeasible in dimensions higher than 5. The common approach is to estimate more restrictive models which are tractable but may not conform to the data. Our contribution is to propose an alternative estimation method that is numerically feasible, produces positive semi-definite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator to a number of existing ones.

Suggested Citation

  • Olivier Ledoit & Pedro Santa Clara & Michael Wolf, 2001. "Flexible multivariate GARCH modeling with an application to international stock markets," Economics Working Papers 578, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:578
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    References listed on IDEAS

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    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. 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 116-131, February.
    3. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    4. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
    5. 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.
    6. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    7. repec:cdl:ucsdec:qt56j4143f is not listed on IDEAS
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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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