This study investigates how foreign investors impact the Taiwanese stock market using the AutoRegressive Jump Intensity (ARJI) model proposed by Chan and Maheu (2002), in which stock volatility in Taiwan is classified as either normal or abnormal and the net purchases of foreign investors, together with the classified volatilities, are included in the bivariate Vector Autoregression (VAR) model for further analyses. The sample period comprises of two parts, namely before and after relaxation of the restrictions on Qualified Foreign Institutional Investor (QFII) investors on 2 October 2003 (pre- and post-QFII). The forecast error variance decompositions and impulse–response functions are obtained via simulating the VAR model. Our results indicate why previous studies, in which abnormal volatilities were not taken into account, confronted biased and inconsistent results. Biased results from previous studies tend to be caused by not differentiating between normal and abnormal volatilities, and the results of this study provide a valuable reference for efforts to end conflicting arguments for whether destabilizing or stabilizing stock markets of foreign investor transactions. Furthermore, the study results also indicate why Taiwan was less affected during the Asian financial crisis.