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

作者：Kristoufek Ladislav^*

来源：Physica A: Statistical Mechanics and Its Applications , 2012, 391(17): 4252-4260.

DOI：10.1016/j.physa.2012.04.005

• Rescaled range analysis
• Modified rescaled range analysis
• Hurst exponent
• Long-term memory
• Short-term memory

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.

• 出版日期2012-9-1