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

TL;DR

This study uses Monte Carlo simulations to evaluate how classical and modified rescaled range analyses perform under different distributional properties and dependence structures, revealing their robustness and biases.

Contribution

It provides a comprehensive analysis of the effects of distributional properties on the accuracy of R/S and M-R/S estimators in detecting long-range correlations.

Findings

R/S is slightly biased upwards for short-range dependence.

M-R/S is strongly biased downwards for long-range dependence.

Both estimators are robust except under extreme kurtosis and skewness.

Abstract

In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations 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 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 8 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.