IDEAS home Printed from https://ideas.repec.org/p/aah/create/2011-24.html
   My bibliography  Save this paper

Conditional Correlation Models of Autoregressive Conditional Heteroskedasticity with Nonstationary GARCH Equations

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/11/rp11_24.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Annastiina Silvennoinen & Timo Teräsvirta, 2017. "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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nguyen, Hoang & Virbickaitė, Audronė, 2023. "Modeling stock-oil co-dependence with Dynamic Stochastic MIDAS Copula models," Energy Economics, Elsevier, vol. 124(C).
    2. Cristina Amado & Annastiina Silvennoinen & Timo Teräsvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," CREATES Research Papers 2018-14, Department of Economics and Business Economics, Aarhus University.
    3. Amado, Cristina & Teräsvirta, Timo, 2014. "Modelling changes in the unconditional variance of long stock return series," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 15-35.
    4. Marcel Wollschlager & Rudi Schafer, 2015. "Impact of non-stationarity on estimating and modeling empirical copulas of daily stock returns," Papers 1506.08054, arXiv.org.
    5. Pilar Gargallo & Luis Lample & Jesús A. Miguel & Manuel Salvador, 2021. "Co-Movements between Eu Ets and the Energy Markets: A Var-Dcc-Garch Approach," Mathematics, MDPI, vol. 9(15), pages 1-36, July.
    6. Prince Osei Mensah & Anokye M. Adam, 2020. "Copula-Based Assessment of Co-Movement and Tail Dependence Structure Among Major Trading Foreign Currencies in Ghana," Risks, MDPI, vol. 8(2), pages 1-20, June.
    7. Hu, Haiqing & Chen, Di & Sui, Bo & Zhang, Lang & Wang, Yinyin, 2020. "Price volatility spillovers between supply chain and innovation of financial pledges in China," Economic Modelling, Elsevier, vol. 89(C), pages 397-413.
    8. Otranto, Edoardo, 2010. "Identifying financial time series with similar dynamic conditional correlation," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 1-15, January.
    9. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    10. Kamel Malik Bensafta & Gervasio Semedo, 2014. "Market Volatility Transmission and Central Banking: What Happened during the Subprime Crisis?," International Economic Journal, Taylor & Francis Journals, vol. 28(4), pages 559-588, December.
    11. Annastiina Silvennoinen & Timo Teräsvirta, 2009. "Modeling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 7(4), pages 373-411, Fall.
    12. Herwartz, Helmut & Golosnoy, Vasyl, 2007. "Semiparametric Approaches to the Prediction of Conditional Correlation Matrices in Finance," Economics Working Papers 2007-23, Christian-Albrechts-University of Kiel, Department of Economics.
    13. Carlo Drago & Andrea Scozzari, 2023. "A Network-Based Analysis for Evaluating Conditional Covariance Estimates," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    14. Gargallo, Pilar & Lample, Luis & Miguel, Jesús & Salvador, Manuel, 2022. "Dynamic comparison of portfolio risk: Clean vs dirty energy," Finance Research Letters, Elsevier, vol. 47(PA).
    15. Gian Piero Aielli, 2011. "Dynamic Conditional Correlation: On properties and estimation," "Marco Fanno" Working Papers 0142, Dipartimento di Scienze Economiche "Marco Fanno".
    16. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    17. Bauwens, Luc & Otranto, Edoardo, 2020. "Nonlinearities and regimes in conditional correlations with different dynamics," Journal of Econometrics, Elsevier, vol. 217(2), pages 496-522.
    18. Carlo Drago & Andrea Scozzari, 2022. "Evaluating conditional covariance estimates via a new targeting approach and a networks-based analysis," Papers 2202.02197, arXiv.org.
    19. Cristina Amado & Timo Teräsvirta, 2017. "Specification and testing of multiplicative time-varying GARCH models with applications," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 421-446, April.
    20. Riadh El Abed & Sahar Boukadida & Warda Jaidane, 2019. "Financial Stress Transmission from Sovereign Credit Market to Financial Market: A Multivariate FIGARCH-DCC Approach," Global Business Review, International Management Institute, vol. 20(5), pages 1122-1140, October.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aah:create:2011-24. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.