Persistent-threshold-GARCH processes: Model and application

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.