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An application of the analogy between vector ARCH and vector random coefficient autoregressive models

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  • He, Changli

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

Abstract

In this paper we derive conditions for the conditional covariance matrix to be positive definite in a general vector ARCH model. The conditions can be easily extended to the diagonal vector GARCH model. For the general vector GARCH model, analytical expressions for the conditions in terms of the parameters become complicated, but their validity can in principle be checked numerically once the values of the parameters are given.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 516.

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Length: 15 pages
Date of creation: 20 Nov 2002
Date of revision:
Handle: RePEc:hhs:hastef:0516

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Keywords: conditional covariance matrix; multivariate GARCH; multivariate volatility model; random coefficient model; volatility forecasting;

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  1. Bera, Anil K & Higgins, Matthew L & Lee, Sangkyu, 1992. "Interaction between Autocorrelation and Conditional Heteroscedasticity: A Random-Coefficient Approach," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 10(2), pages 133-42, April.
  2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(01), pages 122-150, February.
  3. 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, University of Chicago Press, vol. 96(1), pages 116-31, February.
  4. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  5. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 10(2), pages 229-35, April.
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Cited by:
  1. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Goeij, P. C. de & Marquering, W., 2004. "Modeling the conditional covariance between stock and bond returns: A multivariate GARCH approach," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-194709, Tilburg University.
  3. Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 12(1), pages 147-163, 03.
  4. Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Positivity Constraints on the Conditional Variances in the Family of Conditional Correlation GARCH Models," Working Paper Series in Economics and Finance, Stockholm School of Economics 675, Stockholm School of Economics, revised 15 Nov 1007.

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