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In this paper, the researcher proposes a double threshold-IGRACH model to investigate the impacts of foreign investment turnover and exchange rate volatilities on the return volatility for the Taiwan stock market. Empirical result shows that the AR(2)-double threshold-IGRACH(1,1) model is appropriate to be used in investigating how the volatility rates of the foreign investment turnovers and exchange rates affect the Taiwan stock returns, as well as reflects that the Taiwan stock market has an asymmetrical effect. It also shows that the news of the foreign investment turnover and exchange rate volatilities would affect the stock market returns, including its variation risk. The double threshold-IGARCH model, therefore, has more explanatory ability as compared to the SETAR and the GJR-GARCH model.