New Variants Of Dfa Based On Loess And Lowess Methods: Generalization Of The Detrending Moving Average

Proposed early in the 90ies, the detrended fluctuation analysis (DFA) can be used to estimate the Hurst exponent and has been proven relevant in various applications, from economics to biomedical. For the last years, variants have been proposed. They differ in the way to estimate the trend of the centered integrated signal. In this paper, we recall the main principles of some of these methods, provide explanations on the behaviours of the algorithms and analyze the relevance of new variants based on the Savitzky–Golay filter, also known as the LOESS approach, and the LOWESS. They bridge the gap between the DFA and the detrending moving average (DMA). We hence show that the LOESS-based method is a generalization of the DMA.