A fast algorithm of detrending moving average-based scaling analysisand its application to biomedical signals

Abstract

Long-range correlations have been observed in a wide variety of biosignal time series. It has been demonstrated that its alteration is associated with a disease state and higher mortality. Thus, fast and reliable characterization of long-range correlations is an important task. Among scaling analysismethods, it has been demonstrated that higher-order centered detrending moving average (DMA) analysis has good performance. However, a straightforward implementation of higher-order DMA requires a very long computational time. To solve this issue, we introduce a fast algorithm for higher order DMA. Our algorithm can significantly reduce computational cost; the computational time of our algorithm is approximately proportional to the data length, although that of the conventional algorithm is proportional to the square of the data length. Through the analysis of artificial and heart rate variability time series, we discuss possible applications of higher order DMA.