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Conditional Correlation Models of Autoregressive Conditional Heteroskedasticity with Nonstationary GARCH Equations

Author

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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. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-234, April.
    2. 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.
    3. Engle, Robert & Colacito, Riccardo, 2006. "Testing and Valuing Dynamic Correlations for Asset Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 238-253, April.
    4. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
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    Cited by:

    1. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    2. Silvennoinen, Annastiina & Teräsvirta, Timo, 2024. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," Econometrics and Statistics, Elsevier, vol. 32(C), pages 57-72.
    3. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    4. Ngene, Geoffrey & Post, Jordin A. & Mungai, Ann N., 2018. "Volatility and shock interactions and risk management implications: Evidence from the U.S. and frontier markets," Emerging Markets Review, Elsevier, vol. 37(C), pages 181-198.
    5. 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.
    6. Kang‐Soek Lee & Richard A. Werner, 2023. "Are lower interest rates really associated with higher growth? New empirical evidence on the interest rate thesis from 19 countries," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(4), pages 3960-3975, October.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Anthony D. Hall & Annastiina Silvennoinen & Timo Teräsvirta, 2021. "Four Australian Banks and the Multivariate Time-Varying Smooth Transition Correlation GARCH model," CREATES Research Papers 2021-13, Department of Economics and Business Economics, Aarhus University.
    12. 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.
    13. Anthony D. Hall & Annastiina Silvennoinen & Timo Teräsvirta, 2023. "Building Multivariate Time-Varying Smooth Transition Correlation GARCH Models, with an Application to the Four Largest Australian Banks," Econometrics, MDPI, vol. 11(1), pages 1-37, February.
    14. Susana Martins & Cristina Amado, 2018. "Financial Market Contagion and the Sovereign Debt Crisis: A Smooth Transition Approach," NIPE Working Papers 08/2018, NIPE - Universidade do Minho.
    15. 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.
    16. Ngene, Geoffrey M. & Lee Kim, Yea & Wang, Jinghua, 2019. "Who poisons the pool? Time-varying asymmetric and nonlinear causal inference between low-risk and high-risk bonds markets," Economic Modelling, Elsevier, vol. 81(C), pages 136-147.
    17. Campos-Martins, Susana & Amado, Cristina, 2022. "Financial market linkages and the sovereign debt crisis," Journal of International Money and Finance, Elsevier, vol. 123(C).
    18. Yuanyuan Zhang & Rong Liu & Qin Shao & Lijian Yang, 2020. "Two‐Step Estimation for Time Varying Arch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 551-570, July.

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    More about this item

    Keywords

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

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