Mostly used estimators of Hurst exponent for detection of long-range dependence are biased by presence of short-range dependence in the underlying time series. We present confidence intervals estimates for rescaled range and modified rescaled range. We show that the difference in expected values and confidence intervals enables us to use both methods together to clearly distinguish between the two types of processes. Moreover, both methods are robust against the presence of heavy tails in the underlying process.
rescaled range modified rescaled range Hurst exponent long-range dependence confidence intervals