Rescaled range analysis and detrended fluctuation analysis: finite sample properties and confidence intervals
Abstract
We focus on finite sample properties of two mostly used methods of Hurst exponent H estimation-rescaled range analysis (R/S) and detrended fluctuation analysis (DFA). Even though both methods have been widely applied on different types of financial assets, only seve- ral papers have dealt with the 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 to DFA. However, we show that even though the estimates of R/S are truly significantly higher than an asymptotic limit of 0.5, for random time series with lengths from 29 to 217, 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.