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Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process

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  • Liu, Ji-Chun

Abstract

In order to capture three important dynamic characteristics of time series, the asymmetry, regimes, and conditional heteroskedasticity, based on Hwang and Basawa's [2004. Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes. Statist. Probab. Lett. 68, 209-220] and Haas et al. [2004. A new approach to Markov-switching GARCH models. J. Financial Econometrics 2, 493-530] models, this paper proposes a Markov-switching Box-Cox transformed threshold GARCH model. Some structural properties of this new GARCH process are considered. First, a sufficient and necessary condition for the existence of the weakly and strictly stationary solution of the process is presented, respectively. Second, the general conditions for the existence of high-order moments of the process are derived. The technique used in this paper for the weak stationarity and the high-order moments of the process is different from that used in Haas et al. [2004. A new approach to Markov-switching GARCH models. J. Financial Econometrics 2, 493-530], and avoids the assumption that the process started in the infinite past with finite variance.

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  • Liu, Ji-Chun, 2007. "Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1428-1438, July.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:13:p:1428-1438
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    References listed on IDEAS

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    1. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
    2. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    3. Hwang, S. Y. & Woo, Mi-Ja, 2001. "Threshold ARCH(1) processes: asymptotic inference," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 11-20, May.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Liu, Ji-Chun, 2006. "On the tail behaviors of Box-Cox transformed threshold GARCH(1,1) process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1323-1330, July.
    6. Hwang, S. Y. & Basawa, I. V., 2004. "Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 209-220, July.
    7. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
    8. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    9. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    10. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
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    Cited by:

    1. 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.
    2. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
    3. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    4. Haas Markus & Liu Ji-Chun, 2018. "A multivariate regime-switching GARCH model with an application to global stock market and real estate equity returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(3), pages 1-27, June.
    5. Haas, Markus, 2008. "The autocorrelation structure of the Markov-switching asymmetric power GARCH process," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1480-1489, September.
    6. Liu, Ji-Chun, 2012. "Structure of a double autoregressive process driven by a hidden Markov chain," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1468-1473.

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