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The Detrended Fluctuation Analysis (DFA) and its extensions (MF-DFA) have been proposed as robust techniques to determine possible long-range correlations in self-affine signals. However, many studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimations of the scaling exponents. Lately, several modifications of the DFA method have been reported with many different techniques for eliminating the monotonous and periodic trends. In this study, a smoothing algorithm based on the Orthogonal V-system (OVS) is proposed to minimize the effect of power-law trends, periodic trends, assembled trends and piecewise function trends. The effectiveness of the new method is demonstrated on monofractal data and multifractal data corrupted with different trends.

The RR and RT time intervals extracted from the electrocardiogram measure respectively the duration of cardiac cycle and repolarization. The series of these intervals recorded during the exercise test are characterized by two trends: A decreasing one during the stress phase and an increasing one during the recovery, separated by a global minimum. We model these series as a sum of a deterministic trend and random fluctuations, and estimate the trend using methods of curve extraction: Running mean, polynomial fit, multi scale wavelet decomposition. We estimate the minimum location from the trend. Data analysis performed on a group of 20 healthy subjects provides evidence that the minimum of the RR series precedes the minimum of the RT series, with a time delay of about 19 seconds.

The amplitudes of R and T waves of the electrocardiogram (ECG) recorded during the exercise test show both large inter- and intra-individual variability in response to stress. We analyze a dataset of 65 normal subjects undergoing ambulatory test. We model the dataset of R and T series in the framework of functional data, assuming that the individual series are realizations of a non-stationary process, centered at the population trend. We test the time variability of this trend computing a simultaneous confidence band and the zero crossing of its derivative. The analysis shows that the amplitudes of the R and T waves have opposite responses to stress, consisting respectively in a bump and a dip at the early recovery stage. Our findings support the existence of a relationship between R and T wave amplitudes and respectively diastolic and systolic ventricular volumes.