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Flexible Multivariate GARCH Modeling With an Application to International Stock Markets

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  • Ledoit, Olivier
  • Santa-Clara, Pedro
  • Wolf, Michael

Abstract

We develop an estimation method for the Diagonal Multivariate GARCH model. For a vector of size N unidimensional GARCH processes for the diagonal elements of the conditional covariance matrix, and N(N-1)/2 bivariate GARCH processes for the off-diagonal elements of the conditional covariance matrix. The coefficient matrices are then transformed in such a way that ensures the positive semi-definiteness of the conditional covariance matrix. Under a technical assumption, the estimator has the same asymptotic properties as the univariate and bivariate maximum likelihood GARCH estimators. The method is computationally feasible for large problems, of size N=100 or larger. We do not need to impose any particular simplifying structure on the coefficient matrices. The conditional covariance is ensured to be stationary, and is, in general, well conditioned. We provide an empirical application in the context of international stock markets and offer Monte Carlo evidence of the good small sample properties of the model.

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Paper provided by Anderson Graduate School of Management, UCLA in its series University of California at Los Angeles, Anderson Graduate School of Management with number qt93s6p8gb.

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Date of creation: 27 Feb 1999
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Handle: RePEc:cdl:anderf:qt93s6p8gb

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  1. 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.
  2. Engle, Robert F, 2000. "Dynamic Conditional Correlation - A Simple Class of Multivariate GARCH Models," University of California at San Diego, Economics Working Paper Series qt56j4143f, Department of Economics, UC San Diego.
  3. 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.
  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. 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.
  6. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  7. 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.
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