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A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-Varying GARCH Model

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  • Jian Kang

    (School of Finance, Dongbei University of Finance and Economics, Dalian 116025, China)

  • Johan Stax Jakobsen

    (Department of Finance, Copenhagen Business School, DK-2000 Frederiksberg, Denmark
    Center for Research in Econometric Analysis of Time Series (CREATES), Aarhus University, DK-8000 Aarhus, Denmark)

  • Annastiina Silvennoinen

    (National Centre for Econometric Research (NCER), Queensland University of Technology, Brisbane, QLD 4000, Australia)

  • Timo Teräsvirta

    (Center for Research in Econometric Analysis of Time Series (CREATES), Aarhus University, DK-8000 Aarhus, Denmark
    Center for Applied Statistics and Economics (C.A.S.E.), Humboldt-Universität zu Berlin, DE-10178 Berlin, Germany)

  • Glen Wade

    (National Centre for Econometric Research (NCER), Queensland University of Technology, Brisbane, QLD 4000, Australia)

Abstract

We construct a parsimonious test of constancy of the correlation matrix in the multivariate conditional correlation GARCH model, where the GARCH equations are time-varying. The alternative to constancy is that the correlations change deterministically as a function of time. The alternative is a covariance matrix, not a correlation matrix, so the test may be viewed as a general test of stability of a constant correlation matrix. The size of the test in finite samples is studied by simulation. An empirical example involving daily returns of 26 stocks included in the Dow Jones stock index is given.

Suggested Citation

  • Jian Kang & Johan Stax Jakobsen & Annastiina Silvennoinen & Timo Teräsvirta & Glen Wade, 2022. "A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-Varying GARCH Model," Econometrics, MDPI, vol. 10(3), pages 1-41, August.
    • Handle: RePEc:gam:jecnmx:v:10:y:2022:i:3:p:30-:d:896537
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    More about this item

    Keywords

    deterministically varying correlation; multiplicative time-varying GARCH; multivariate GARCH; nonstationary volatility; smooth transition GARCH;
    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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