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Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations


  • Annastiina Silvennoinen

    (School of Economics and Finance, Queensland University of Technology)

  • Timo Teräsvirta

    (Department of Economic Statistics, Stokholm School of Economics)


In this paper we propose a new multivariate GARCH model with time-varying conditional correlation structure. The approach adopted here is based on the decomposition of the covariances into correlations and standard deviations. The time-varying conditional correlations change smoothly between two extreme states of constant correlations according to an endogenous or exogenous transition variable. An LM test is derived to test the constancy of correlations and LM and Wald tests to test the hypothesis of partially constant correlations. Analytical expressions for the test statistics and the required derivatives are provided to make computations feasible. An empirical example based on daily return series of five frequently traded stocks in the Standard & Poor 500 stock index completes the paper. The model is estimated for the full five-dimensional system as well as several subsystems and the results discussed in detail.

Suggested Citation

  • Annastiina Silvennoinen & Timo Teräsvirta, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," Research Paper Series 168, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:168

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    More about this item


    multivariate GARCH; constant conditional correlation; dynamic conditional correlation; return comovement; variable correlation GARCH model; volatility model evaluation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G1 - Financial Economics - - General Financial Markets

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