On the Estimation of the Hurst Exponent Using Adjusted Rescaled Range Analysis, Detrended Fluctuation Analysis and Variance Time Plot: A Case of Exponential Distribution

Hurst Exponent has been widely used in different fields as a measure of long range dependence in time series. It has been studied in hydrology and geophysics, economics and finance, and recently, it is still a hot topic in the different areas of research involving DNA sequences, cardiac dynamics, internet traffic, meteorology and geology. Various methods in the estimation of Hurst Exponent have been proposed such as Adjusted Rescaled Range Analysis, Detrended Fluctuation Analysis and Variance Time Plot Analysis. This study explored the efficiency of the three methods: Adjusted Rescaled Range Analysis, Detrended Fluctuation Analysis and Variance Time Plot Analysis in the estimation of Hurst Exponent when data are generated from an exponential distribution. In addition, the efficiency of the three methods was compared in different sample sizes of 128, 256, 512, 1024 and varying λ parameter values of 0.1, 0.5, 1.5, 3.0, 5.0 and 7.0. The estimation process for each of the methods using different sample sizes and λ parameter values were repeated for 100, 500 and 1000 times to verify the consistency of the result. A Scilab Program containing different functions was developed for the study to aid in the simulation process and calculation. The Adjusted Rescaled Range Analysis was the most efficient method with the smallest Mean Square Error for all λ parameter values and different sample sizes.