A fractal analysis of foreign exchange markets

Long memory in foreign exchange markets is examined for the post-Bretton Woods period using Lo 's [1991] modified rescaled range (R/S). Conventional R/S techniques are presented for comparison. Unlike conventional techniques, Lo's analysis is robust to short-term dependence and conditional heteroskedasticity. Significant long memory and fractal structure are conclusively demonstrated for all 22 countries studied, indicating that traditional econometric methods are inadequate for analyzing foreign exchange markets. However, shortterm dependence and conditional heteroskedasticity are also present, making it difficult to describe the nature of the long memory process or processes in foreign exchange markets. The average nonperiodic cycle ranges from 7 months for Canada and the United Kingdom, to approximately 20 months for Austria, Finland, France, Germany, Ireland, Japan, Malaysia, Netherlands, Sweden, and Switzerland. No support is found for the efficient market hypothesis. Results broadly agree with those provided by less sophisticated, less robust R/S methodologies and suggest the possibility that traditional technical analysis should be able to achieve systematic positive returns. (JEL G15).