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

Author

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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.

Suggested Citation

  • He, Changli & Teräsvirta, Timo, 2002. "An application of the analogy between vector ARCH and vector random coefficient autoregressive models," SSE/EFI Working Paper Series in Economics and Finance 516, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0516
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    References listed on IDEAS

    as
    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. 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, vol. 10(2), pages 133-142, April.
    3. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
    4. 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.
    5. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Nakatani, Tomoaki & Teräsvirta, Timo, 2008. "Positivity constraints on the conditional variances in the family of conditional correlation GARCH models," Finance Research Letters, Elsevier, vol. 5(2), pages 88-95, June.
    2. Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 147-163, March.
    3. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2020. "Multivariate leverage effects and realized semicovariance GARCH models," Journal of Econometrics, Elsevier, vol. 217(2), pages 411-430.
    4. de Goeij, P. C. & Marquering, W., 2004. "Modeling the conditional covariance between stock and bond returns : A multivariate GARCH approach," Other publications TiSEM 94fe5ada-715a-4339-b94c-f, Tilburg University, School of Economics and Management.
    5. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.

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    More about this item

    Keywords

    conditional covariance matrix; multivariate GARCH; multivariate volatility model; random coefficient model; volatility forecasting;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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