  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 {\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 using
different sample sizes and {\lambda} 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 {\lambda}
parameter values and different sample sizes.
