This paper presents a test for long-range memory in stock market prices that is robust to short-range dependence. The test is a modification of the R/S statistic, which was originally proposed by Hurst and later refined by Mandelbrot. The modified R/S statistic is derived using functional central limit theory and is applied to daily, weekly, monthly, and annual stock return indexes over several time periods. The results show that there is no evidence of long-range dependence in any of the indexes over any sample period or sub-period once short-term autocorrelations are taken into account. Monte Carlo experiments indicate that the modified R/S test has power against at least two specific models of long-run memory, suggesting that stochastic models of short-range dependence may adequately capture the time series behavior of stock returns. The paper discusses the distinction between long-range and short-range dependence, and presents the classical R/S statistic. It then introduces the modified R/S statistic and develops its asymptotic sampling theory. The results of the empirical investigation are reported, and the size and power of the test are discussed. The paper concludes that there is little support for long-term memory in stock returns, and that the data are consistent with the null hypothesis of short-range dependence. The findings suggest that the long-run predictability of stock returns uncovered by previous studies may not be "long-run" in the time series sense, but may be the result of more conventional models of short-range dependence.This paper presents a test for long-range memory in stock market prices that is robust to short-range dependence. The test is a modification of the R/S statistic, which was originally proposed by Hurst and later refined by Mandelbrot. The modified R/S statistic is derived using functional central limit theory and is applied to daily, weekly, monthly, and annual stock return indexes over several time periods. The results show that there is no evidence of long-range dependence in any of the indexes over any sample period or sub-period once short-term autocorrelations are taken into account. Monte Carlo experiments indicate that the modified R/S test has power against at least two specific models of long-run memory, suggesting that stochastic models of short-range dependence may adequately capture the time series behavior of stock returns. The paper discusses the distinction between long-range and short-range dependence, and presents the classical R/S statistic. It then introduces the modified R/S statistic and develops its asymptotic sampling theory. The results of the empirical investigation are reported, and the size and power of the test are discussed. The paper concludes that there is little support for long-term memory in stock returns, and that the data are consistent with the null hypothesis of short-range dependence. The findings suggest that the long-run predictability of stock returns uncovered by previous studies may not be "long-run" in the time series sense, but may be the result of more conventional models of short-range dependence.