A Modified GARCH Model with Spells of Shocks

The GARCH model is modified to capture the effect on volatilities of the consecutive number of positive or negative shocks. The new model is tested against the Shanghai Shcomp and Nikkei225 indices and found particularly useful in analyzing the Shcomp index. Similarly, the EGARCH model is extended along the same line as the GARCH model and is applied to the same sets of data. Stationarity of the new GARCH (1, 1) model is proved, and also derived is the asymptotic distribution of the quasi-maximum likelihood estimator.