R/S analysis and DFA: finite sample properties and confidence intervals

We focus on finite sample properties of two mostly used methods of Hurst exponent H estimation – R/S analysis and DFA. Even though both methods have been widely applied on different types of financial assets, only several papers have dealt with finite sample properties which are crucial as the properties differ significantly from the asymptotic ones. Recently, R/S analysis has been shown to overestimate H when compared with DFA. However, we show on the random time series with lengths from 2^9 to 2^17 that even though the estimates of R/S are truly significantly higher than an asymptotic limit of 0.5, they remain very close to the estimates proposed by Anis & Lloyd and the estimated standard deviations are lower than the ones of DFA. On the other hand, DFA estimates are very close to 0.5. The results propose that R/S still remains useful and robust method even when compared to newer method of DFA which is usually preferred in recent literature.rescaled range analysis, detrended fluctuation analysis, Hurst exponent, long-range dependence, confidence intervals