Abstract Detrended fluctuation analysis (DFA) is a scaling method commonly used for detecting long-range correlations in nonstationary time series. Applications range from financial time series to physiological data. However, as the removal of trends in DFA is based on discontinuous polynomial fitting, oscillations in the fluctuation function and significant errors in crossover locations can be introduced. To reduce the problems induced by discontinuous fitting, moving average (MA) methods have been proposed previously by Alesio et al. (Eur. J. Phys. B 27 (2002) 197). In this work, a variant of such MA methods is studied; specifically, the performance and characteristics of a MA method based on central differences is studied. Some important properties of this MA method are analyzed and illustrated with several artificial and real time series.