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Hurst Exponent has been widely used in different fields as a measure of longrange dependence in time series. It has been studied in hydrology andgeophysics, economics and finance, and recently, it is still a hot topic in thedifferent areas of research involving DNA sequences, cardiac dynamics, internettraffic, meteorology and geology. Various methods in the estimation of HurstExponent have been proposed such as Adjusted Rescaled Range Analysis, DetrendedFluctuation Analysis and Variance Time Plot Analysis. This study explored theefficiency of the three methods: Adjusted Rescaled Range Analysis, DetrendedFluctuation Analysis and Variance Time Plot Analysis in the estimation of HurstExponent when data are generated from an exponential distribution. In addition,the efficiency of the three methods was compared in different sample sizes of128, 256, 512, 1024 and varying {\lambda} parameter values of 0.1, 0.5, 1.5,3.0, 5.0 and 7.0. The estimation process for each of the methods usingdifferent sample sizes and {\lambda} parameter values were repeated for 100,500 and 1000 times to verify the consistency of the result. A Scilab Programcontaining different functions was developed for the study to aid in thesimulation process and calculation. The Adjusted Rescaled Range Analysis wasthe most efficient method with the smallest Mean Square Error for all {\lambda}parameter values and different sample sizes.

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