Long term dependence in stock returns

We show, using the modified rescaled range statistic, that none of the return series of indices of five European countries, the United States and Japan exhibits long term dependence. This statistic — introduced by Lo (1991) — correct Hurst's (1951) ‘classical’ rescaled range statistic for short term dependence. We also report the classical rescaled range statistic after adjusting the series for short term dependence. This procedure shows, for cases where the results of the modified rescaled range statistic are mixed, that no long term dependence can be found. Simulations indicate reasonable power of this adjustment procedure. Furthermore, we find that estimates of the Hurst exponent, a related measure of long term dependence, are also biased by short term dependence. Simulations show that this measure — that has recently attracted growing interest — cannot distinguish between models with or without long term dependence.