Leave One Out Detrended Fluctuation Analysis

Abstract

A relevant issue in time series analysis is the estimation of long-range dependence, that is, how much future values of a time series depend on current values. One of the ways to verify this dependence is by estimating the Hurst exponent using methods such as detrended fluctuation analysis. Here, we propose a new methodology to estimate the Hurst exponent, named leave one out detrended fluctuation analysis. Furthermore, based on this new estimator for the Hurst exponent, we propose the noise reduction by the leave one out detrended fluctuation analysis method. We apply this new denoising method to electrocardiogram noise reduction. The results presented in this work show that this new methodology outperforms the SureShrink and universal noise reduction methods.