Impact of scaling range on the effectiveness of detrending methods

Abstract: We make the comparative study of scaling range properties for detrended fluctuation analysis (DFA), detrended moving average analysis (DMA) and recently proposed new technique called modified detrended moving average analysis (MDMA). Basic properties of scaling ranges for these techniques are reviewed. The efficiency and exactness of all three methods towards proper determination of scaling exponent $H$ is discussed, particularly for short series of uncorrelated or persistent data. \end{abstract}