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Conditional Correlation Models of Autoregressive Conditional Heteroskedasticity with Nonstationary GARCH Equations

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  • Cristina Amado

    () (University of Minho and NIPE)

  • Timo Teräsvirta

    () (Aarhus University, School of Economics and Management and CREATES)

Abstract

In this paper we investigate the effects of careful modelling the long-run dynamics of the volatil- ities of stock market returns on the conditional correlation structure. To this end we allow the individual unconditional variances in Conditional Correlation GARCH models to change smoothly over time by incorporating a nonstationary component in the variance equations. The modelling technique to determine the parametric structure of this time-varying component is based on a sequence of specification Lagrange multiplier-type tests derived in Amado and Teräsvirta (2011). The variance equations combine the long-run and the short-run dynamic behaviour of the volatilities. The structure of the conditional correlation matrix is assumed to be either time independent or to vary over time. We apply our model to pairs of seven daily stock returns belonging to the S&P 500 composite index and traded at the New York Stock Exchange. The results suggest that accounting for deterministic changes in the unconditional variances considerably improves the fit of the multivariate Conditional Correlation GARCH models to the data. The effect of careful specification of the variance equations on the estimated correlations is variable: in some cases rather small, in others more discernible. As a by-product, we generalize news impact surfaces to the situation in which both the GARCH equations and the conditional correlations contain a deterministic component that is a function of time.

Suggested Citation

  • Cristina Amado & Timo Teräsvirta, 2011. "Conditional Correlation Models of Autoregressive Conditional Heteroskedasticity with Nonstationary GARCH Equations," CREATES Research Papers 2011-24, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-24
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    References listed on IDEAS

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    1. Van Bellegem, Sebastien & von Sachs, Rainer, 2004. "Forecasting economic time series with unconditional time-varying variance," International Journal of Forecasting, Elsevier, vol. 20(4), pages 611-627.
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    1. repec:eee:econom:v:204:y:2018:i:2:p:223-247 is not listed on IDEAS
    2. De Santis, Roberto A. & Stein, Michael, 2015. "Financial indicators signaling correlation changes in sovereign bond markets," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 86-102.
    3. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    4. Darolles, Serges & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," MPRA Paper 83988, University Library of Munich, Germany.
    5. De Santis, Roberto A. & Stein, Michael, 2016. "Correlation changes between the risk-free rate and sovereign yields of euro area countries," Working Paper Series 1979, European Central Bank.
    6. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    7. Annastiina Silvennoinen & Timo Teräsvirta, 3108. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.
    8. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    9. Bekiros, Stelios D., 2014. "Contagion, decoupling and the spillover effects of the US financial crisis: Evidence from the BRIC markets," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 58-69.
    10. De Santis, Roberto A. & Stein, Michael, 2014. "Financial indicators signalling correlation changes in sovereign bond markets," Working Paper Series 1746, European Central Bank.
    11. Guerello, Chiara, 2016. "The effect of investors’ confidence on monetary policy transmission mechanism," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 248-266.

    More about this item

    Keywords

    Multivariate GARCH model; Time-varying unconditional variance; Lagrange multiplier test; Modelling cycle; Nonlinear time series.;

    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

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