Nonparametric segmentation of nonstationary time series

Abstract

The nonstationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasistationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption of stationarity, it is important to detect in real time series intervals holding that property. With that aim, we introduce a segmentation algorithm based on a fully nonparametric approach. We illustrate its applicability through the analysis of real time series presenting diverse degrees of nonstationarity, thus showing that this segmentation procedure generalizes and allows one to uncover features unresolved by previous proposals based on the discrepancy of low order statistical moments only.

Diminished heart beat non-stationarities in congestive heart failure

“…The critical value is given by the empirical expression $D_{\text{crit}}^{\text{max}}(n)=a{(\ln n-b)}^c,$ ( a , b , c ) = (1.52, 1.80, 0.14) for P 0 = 0.95, n = n L + n R . Equation (2) was obtained by determining D max of a large number of sequences of n independent and identically distributed Gaussian numbers, and then, using the complementary cumulative distribution of D max , we found the critical values for each significance level (Camargo et al, 2011). …”

“…Since the mean based segmentation has t -statistics computed for equal variance samples as the criterion for locating the cutting points, no information about the variances could be inferred. Instead of testing the difference for the mean, we perform a non-parametric segmentation (Camargo et al, 2011), taking into account the whole distribution, with all moments, e.g., mean and variance. In the case of HRV, the known amplitude-frequency coupling of the dominant short-term oscillation, the respiratory sinus-arrhythmia, connects the changes in the variance with the time-dependent covariance, implying non-stationarity (Hirsch and Bishop, 1981).…”

Quantification of heart beat nonstationarities by nonparametric segmentation

“…See Ref. [3] for further details. We performed the KSsegmentation with L 0 =30 sample points in correspondence to the defined higher edge frequency of the very low frequency (VLF) band of heart rate with 0.03 Hz [1] providing at least a half period of this frequency in each segment.…”

“…The idea of the segmentation applied to time series is to provide patches of the signal where stationarity is verified. Instead of testing only the difference for the mean [2], we perform a nonparametric segmentation [3], taking into account the whole distribution, with all moments, especially mean and variance. We also use the known amplitude-frequency coupling of the dominant short-term oscillation [4], the respiratory sinusarrhythmia, which connects the changes in the variance with the time-dependent covariance, implying nonstationarity.…”

Algebraic segmentation of short nonstationary time series based on evolutionary prediction algorithms

“…In general, a proper segmentation of a time series provides a useful portrait of the local properties for investigating and modeling nonstationary systems [1]. Such segmentation serves as a valuable tool in different areas including physics [2][3][4], biology [5][6][7], image and signal processing [8,9] and other disciplines.…”