The fractal structure in multinational stock returns

The essence of fractal analysis is seeking for a pattern that is independent of scale. This paper examines the existence of long-term memory in nine Asian stock markets together with US and UK indices using the modified rescaled-ranged (R/S) statistic. The modified R/S statistic is robust not only with respect to the normality assumption,but also to short-term autocorrelation. The data in the sample range from 1 January 1988 to 30 June 1992 and are arranged in daily, weekly and monthly returns. In most cases, the phenomenon of long-term memory is not found; hence the random walk hypothesis cannot be rejected.The UK market, however, exhibits some long-term memory for various data frequencies and lags. The result of this paper provides directions for future research.