Automatic Crossover Detection of Long-Range Correlation Analysis Based on Detrending Operation

A crossover of two scaling regimes is often observed in long-range correlation analysis of time series. This paper proposes a method to accurately detect such crossover points in detrended fluctuation analysis (DFA) and detrending moving average analysis (DMA), which have been widely used to assess long-range correlations. It is known that the detrending operation used in those methods induces time-scale distortion. Our method corrects the scale distortion based on the frequency response of the detrending operation in DFA and DMA and automatically detects the crossover using segmented regression and kernel density estimation. Using the auto-regressive fractionally integrated moving average process, we generate numerical time series showing crossover phenomena and demonstrate the superior performance of our method.