Minimizing periodic trends by applying Laplace transform. (English) Zbl 1219.37055

Summary: Rescaled range analysis (R/S analysis), detrended fluctuation analysis (DFA) and detrended moving average (DMA) are widely-used methods for detection of long-range correlations in time series. Detrended cross-correlation analysis (DCCA) is a recently developed method to quantify the cross-correlations of two non-stationary time series. Another method for studying auto-correlations and cross-correlations was presented by Sergio Arianos and Anna Carbone in 2009. Recent studies have reported the susceptibility of this methods to periodic trends, which can result in spurious crossovers. In this paper, we propose the modified methods base on Laplace transform to minimizing the effect of periodic trends. The effectiveness of our techniques are demonstrated on stock data corrupted with periodic trends.


37M10 Time series analysis of dynamical systems
44A10 Laplace transform
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