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This paper studies the persistence of daily returns of 21 German stocks from 1960 to 2008. We apply a widely used test based upon the modified R/S-Method by Lo [1991]. As an extension to Lux [1996] and Carbone et al. [2004] and in analogy to moving average or moving volatility, the statistics is calculated for moving windows of length 4, 8, and 16 years for every time series. Periods of persistence or long memory in returns can be found in some but not all time series. Robustness of results is verified by investigating stationarity and short memory effects.

Persistence of stock returns is an extensively studied and discussed theme in the analysis of financial markets. Antipersistence is usually attributed to volatilities. However, not only volatilities but also stock returns can exhibit antipersistence. Antipersistent noise has a somewhat rougher appearance than Gaussian noise. Heuristically spoken, price movements are more likely followed by movements in the opposite direction than in the same direction. The pertaining integrated process exhibits a smaller range prices seem to stay in the vicinity of the initial value. We apply a widely used test based upon the modified R/S-Method by Lo [1991] to daily returns of 21 German stocks from 1960 to 2008. Combining this test with the concept of moving windows by Carbone et al. [2004], we are able to determine periods of antipersistence for some of the series under examination. Our results suggest that antipersistence can be found for stocks and periods where extraordinary corporate actions such as mergers & acquisitions or financial distress are present. These effects should be properly accounted for when choosing and designing models for inference.