This paper reports tests of the martingale difference hypothesis (MDH) for the returns of UK stock indices and sterling exchange rates obtained from two modelling perspectives. First, a wide range of conventional approaches to testing the MDH in economic and financial time series are briefly reviewed. These tests are then applied to daily data on four major FTSE stock indices and four major sterling exchange rates. The empirical results show that the MDH is rejected for three of the eight series. Second, the statistics of drawdowns, which measure cumulative losses over an elastic time scale, are applied to examine the martingale behaviour of the stock indices and exchange rates. If successive price variations (returns) are uncorrelated, then drawdowns will distribute as a stretched exponential or, equivalently, any departures from this distribution will suggest the existence of dependencies in returns. Dependencies in large cumulative returns are detected for all return series except the euro, for which only a relatively short history of data is available. After considering the advantages and limitations of the two approaches, it is concluded that the returns of all the series analysed are dependent, especially during financial market crashes.

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