Recently introduced Detrended Moving Average (DMA) method is examined to calculate Holder-Hurst exponent for artificial stochastic time series of various length. Good agreement with Detrended Fluctuation Analysis (DMA) method is confirmed for long time series (N>=3x10⁴), however for shorter series disagreements are found. We show on a statistical basis of 10³-10⁵ time series, representing artificial arithmetic and geometric Brownian motion of a given length, how results of DMA and DFA methods relate to each other. Finally, the new method called Modified Detrended Moving Average Analysis (MDMA)is introduced which gives Holder-Hurst exponent results much closer to DFA method than DMA analysis does. It might be of a big importance, especially for short time series or if sufficient number of data in a time series is not avilable.