Recently introduced Detrended Moving Average (DMA) method is examined and compared with Detrended Fluctuation Analysis (DFA) technique for artificial stochastic Brownian time series of various length  L \sim 10³ \div 10⁵. Our analysis reveals some statistical properties of the Hurst exponent values measured with the use of DFA and DMA methods. Good agreement between DFA and DMA techniques is found for long time series  L\sim 10⁵, however for shorter series two methods are clearly distinguishable. No clear systematic relation previously postulated in literature between DFA and DMA results is found. However, it is shown that on the average, DMA method gives overestimation of the Hurst exponent compared with DFA technique.

PACS numbers: 05.40.Jc, 05.45.Tp, 89.65.Gh, 89.75.Da