The nonlinear relationships between stock indexes and exchange rates

The Lagrange multiplier (LM) principle is used to study the causality in variance and the relationships between the stock indexes and exchange rates of Brazil, Russia, India, and China (BRIC). Weekly closing prices from February 2002 to December 2013 are used for the analysis. The full study period is divided into two sub-periods after the Chow breakpoint test and Quandt–Andrews unknown breakpoint test. The causality is from exchange rate to stock in the first sub-period and no causality relationship between stock index and exchange rate in the second sub-period for Brazil. The causality is from stock index to exchange rate in both the first sub-period and the second sub-period for Russia. The causality is from exchange rate to stock index in both the first sub-period and the second sub-period for India. There is no causality relationship between stock index and exchange rate in the first sub-period, and from exchange rate to stock index in the second sub-period for China. The study results support the argument that volatility can be transmitted between stock index and exchange rate even when the returns of these two variables are either statistically uncorrelated or exhibit no causality in means.