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Persistent-threshold-GARCH processes: Model and application

Author

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  • Park, J.A.
  • Baek, J.S.
  • Hwang, S.Y.

Abstract

Threshold models in the context of conditionally heteroscedastic time series have been found to be useful in analyzing asymmetric volatilities. While the effect of current volatility on the future volatility decreases to zero at an exponential rate for standard-threshold-GARCH (TGARCH) processes, here we introduce a class of TGARCH processes exhibiting persistent properties for which current volatility constantly remains in the future volatilities for all-step ahead forecasts. Analogously to IGARCH (cf. [Nelson, D.B., 1990. Stationarity and persistence in the GARCH(1, 1) model. Econometric Theory 6, 318-334]), our model will be referred to as integrated-TGARCH (I-TGARCH, hereafter). Some theoretical aspects of I-TGARCH processes are discussed. It is also verified that the I-TGARCH class provides a random quantity for limiting cumulative impulse response (cf. [Baillie, R.T., Bollerslev, T., Mikkelsen, H.O., 1996. Fractionally integrated generalized autoregressive conditional heteroskedasticity. J. Econom. 74, 3-30]), indicating persistency in variance. The Korea stock price index (KOSPI) data are analyzed to illustrate applicability of the first order I-TGARCH model.

Suggested Citation

  • Park, J.A. & Baek, J.S. & Hwang, S.Y., 2009. "Persistent-threshold-GARCH processes: Model and application," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 907-914, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:907-914
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    References listed on IDEAS

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    1. Pan, Jiazhu & Wang, Hui & Tong, Howell, 2008. "Estimation and tests for power-transformed and threshold GARCH models," Journal of Econometrics, Elsevier, vol. 142(1), pages 352-378, January.
    2. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-274, May-June.
    3. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
    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. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    8. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    9. 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.
    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. Yuzhi Cai & Julian Stander, 2020. "The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 395-424.
    2. Hwang, S.Y. & Baek, J.S. & Park, J.A. & Choi, M.S., 2010. "Explosive volatilities for threshold-GARCH processes generated by asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 26-33, January.
    3. Kim, Yujin & Hwang, Eunju, 2018. "A dynamic Markov regime-switching GARCH model and its cumulative impulse response function," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 20-30.

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