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Persistent-threshold-GARCH processes: Model and application

Listed author(s):
  • Park, J.A.
  • Baek, J.S.
  • Hwang, S.Y.
Registered author(s):

    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.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 79 (2009)
    Issue (Month): 7 (April)
    Pages: 907-914

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    Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:907-914
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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. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
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