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This research examined the time series characteristics of stock price indices for Hong Kong, Tokyo, New York (NYSE) and London (FTSE) equity markets or stock exchanges during the period of 1991 to 2012. Specifically, we calculate the rate of return and the volatility of return for all the markets and estimate the serial correlation and co-movement of the four markets. We find that the average rate of return varies dramatically for the four equity markets and across time. Further, we find that stock prices are positively serially correlated in general. In the multivariate regressions, we find that there is little evidence to show that either the rate of return in certain markets universally affects the rate of return in other equity markets. It suggests that the four markets are co-integrated but not universally across time and with each other in pairwise dimensions. Lastly, we studied and made conclusions concerning the mean and variation in the volatility of the rates of return in the four equity markets studied.