How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study

In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlation detection — classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently distinguish between short-term memory and long-term memory. To do so, we analyze the behavior of the estimators for independent, short-range dependent, and long-range dependent processes with innovations from eight different distributions. We find that apart from a combination of very high levels of kurtosis and skewness, both estimators are quite robust to distributional properties. Importantly, we show that R / S is biased upwards (yet not strongly) for short-range dependent processes, while M - R / S is strongly biased downwards for long-range dependent processes regardless of the distribution of innovations.