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Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets

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  • Haas, Markus
  • Liu, Ji-Chun

Abstract

We consider a multivariate Markov-switching GARCH model which allows for regime-specific volatility dynamics, leverage effects, and correlation structures. Stationarity conditions are derived, and consistency of the maximum likelihood estimator (MLE) is established under the assumption of Gaussian innovations. A Lagrange Multiplier (LM) test for correct specification of the correlation dynamics is devised, and a simple recursion for computing multi-step-ahead conditional covariance matrices is provided. The theory is illustrated with an application to global stock market and real estate equity returns. The empirical analysis highlights the importance of the conditional distribution in Markov-switching time series models. Specifications with Student's t innovations dominate their Gaussian counterparts both in- and out-of-sample. The dominating specification appears to be a two-regime Student's t process with correlations which are higher in the turbulent (high-volatility) regime.

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  • Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.
    • Handle: RePEc:zbw:vfsc15:112855
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    1. 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.
    2. Nakatani, Tomoaki & Teräsvirta, Timo, 2008. "Positivity constraints on the conditional variances in the family of conditional correlation GARCH models," Finance Research Letters, Elsevier, vol. 5(2), pages 88-95, June.
    3. Mittnik, Stefan, 2014. "VaR-implied tail-correlation matrices," Economics Letters, Elsevier, vol. 122(1), pages 69-73.
    4. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    5. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    6. Christian Francq & Michel Roussignol & Jean‐Michel Zakoian, 2001. "Conditional Heteroskedasticity Driven by Hidden Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 197-220, March.
    7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    8. David Ardia, 2009. "Bayesian estimation of a Markov-switching threshold asymmetric GARCH model with Student-t innovations," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 105-126, March.
    9. Haas, Markus, 2010. "Covariance forecasts and long-run correlations in a Markov-switching model for dynamic correlations," Finance Research Letters, Elsevier, vol. 7(2), pages 86-97, June.
    10. Warren Dean & Robert Faff, 2008. "Evidence of feedback trading with Markov switching regimes," Review of Quantitative Finance and Accounting, Springer, vol. 30(2), pages 133-151, February.
    11. Yen-Hsien Lee, 2014. "An international analysis of REITs and stock portfolio management based on dynamic conditional correlation models," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 28(2), pages 165-180, May.
    12. Brad Case & Massimo Guidolin & Yildiray Yildirim, 2014. "Markov Switching Dynamics in REIT Returns: Univariate and Multivariate Evidence on Forecasting Performance," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 42(2), pages 279-342, June.
    13. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
    14. Olivier Ledoit & Pedro Santa-Clara & Michael Wolf, 2003. "Flexible Multivariate GARCH Modeling with an Application to International Stock Markets," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 735-747, August.
    15. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    16. Francq, Christian & Zakoïan, Jean-Michel, 2012. "Qml Estimation Of A Class Of Multivariate Asymmetric Garch Models," Econometric Theory, Cambridge University Press, vol. 28(1), pages 179-206, February.
    17. He, Changli & Teräsvirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, vol. 20(5), pages 904-926, October.
    18. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
    19. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    20. Ji-Chun Liu, 2006. "Stationarity of a Markov-Switching GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 573-593.
    21. Monica Billio & Massimiliano Caporin, 2005. "Multivariate Markov switching dynamic conditional correlation GARCH representations for contagion analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(2), pages 145-161, November.
    22. Abramson, Ari & Cohen, Israel, 2007. "On The Stationarity Of Markov-Switching Garch Processes," Econometric Theory, Cambridge University Press, vol. 23(3), pages 485-500, June.
    23. Maria Kasch & Massimiliano Caporin, 2013. "Volatility Threshold Dynamic Conditional Correlations: An International Analysis," Journal of Financial Econometrics, Oxford University Press, vol. 11(4), pages 706-742, September.
    24. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    25. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    26. Massimo Guidolin, 2011. "Markov Switching Models in Empirical Finance," Advances in Econometrics, in: Missing Data Methods: Time-Series Methods and Applications, pages 1-86, Emerald Group Publishing Limited.
    27. Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 147-163, March.
    28. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    29. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, vol. 70(1), pages 127-157, January.
    30. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    31. Giacomini, Raffaella & Gottschling, Andreas & Haefke, Christian & White, Halbert, 2008. "Mixtures of t-distributions for finance and forecasting," Journal of Econometrics, Elsevier, vol. 144(1), pages 175-192, May.
    32. Daniel R. Smith, 2008. "Evaluating Specification Tests for Markov‐Switching Time‐Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(4), pages 629-652, July.
    33. Edoardo Otranto, 2010. "Asset allocation using flexible dynamic correlation models with regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 325-338.
    34. Tse, Y. K., 2000. "A test for constant correlations in a multivariate GARCH model," Journal of Econometrics, Elsevier, vol. 98(1), pages 107-127, September.
    35. Michael McAleer & Suhejla Hoti & Felix Chan, 2009. "Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 422-440.
    36. Jan Bulla, 2010. "Hidden Markov models with t components. Increased persistence and other aspects," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 459-475.
    37. Kofman, Paul & Koedijk, Kees & Campbell, Rachel, 2002. "Increased Correlation in Bear markets: A Downside Risk Perspective," CEPR Discussion Papers 3172, C.E.P.R. Discussion Papers.
    38. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826, Elsevier.
    39. Lejeune, Bernard, 2009. "A diagnostic m-test for distributional specification of parametric conditional heteroscedasticity models for financial data," Journal of Empirical Finance, Elsevier, vol. 16(3), pages 507-523, June.
    40. Ardia, David, 2009. "Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations in R," MPRA Paper 17414, University Library of Munich, Germany.
    41. Ramchand, Latha & Susmel, Raul, 1998. "Volatility and cross correlation across major stock markets," Journal of Empirical Finance, Elsevier, vol. 5(4), pages 397-416, October.
    42. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    43. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    44. C. S. Wong & W. S. Chan & P. L. Kam, 2009. "A Student t-mixture autoregressive model with applications to heavy-tailed financial data," Biometrika, Biometrika Trust, vol. 96(3), pages 751-760.
    45. Heaney, Richard & Sriananthakumar, Sivagowry, 2012. "Time-varying correlation between stock market returns and real estate returns," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 583-594.
    46. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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