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Abstract: In this paper, we investigate the persistence of British stock returns over the period 1962-98 using the Variance Ratio (VR) test to check for short-range dependence and the Modified Rescaled Range (MRS) test to check for long-range dependence. A central contribution of the paper is that we investigate the role of the great rebound in stock prices in January 1975 and the crash of October 1987. These shocks, which together represent less than 1% of the data fundamentally alter the time series properties of the data, with extreme skewness, excess kurtosis, and ARCH present in the unadjusted data, but absent from much of the shock-purged data. The VR and MRS tests reveal relatively little evidence of persistence in the original data. However, the VR tests exhibit systematic and significant reversals of sign as between the original and the shock-purged data. It appears that stock prices in Britain persistently stayed away from the mean, and then reverted back towards it in just two excepti...