Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations

Abstract

Fluctuation Analysis (FA) and specially Detrended Fluctuation Analysis (DFA) are techniques commonly used to quantify correlations and scaling properties of complex time series such as the observable outputs of great variety of dynamical systems, from Economics to Physiology. Often, such correlated time series are analyzed using the magnitude and sign decomposition, i.e., by using FA or DFA to study separately the sign and the magnitude series obtained from the original signal. This approach allows for distinguishing between systems with the same linear correlations but different dynamical properties. However, here we present analytical and numerical evidence showing that FA and DFA can lead to spurious results when applied to sign and magnitude series obtained from power-law correlated time series of fractional Gaussian noise (fGn) type. Specifically, we show that: (i) the autocorrelation functions of the sign and magnitude series obtained from fGns are always power-laws; However, (ii) when the sign series presents power-law anticorrelations, FA and DFA wrongly interpret the sign series as purely uncorrelated; Similarly, (iii) when analyzing power-law correlated magnitude (or volatility) series, FA and DFA fail to retrieve the real scaling properties, and identify the magnitude series as purely uncorrelated noise; Finally, (iv) using the relationship between FA and DFA and the autocorrelation function of the time series, we explain analytically the reason for the FA and DFA spurious results, which turns out to be an intrinsic property of both techniques when applied to sign and magnitude series.

Classification of glucose records from patients at diabetes risk using a combined permutation entropy algorithm

“…SampEn also needs three input parameters, N , m, and a threshold r, but it is much more sensitive to these input values than PE, since a suboptimal choice of these values can lead to incorrect results [28]. DFA is also quite unstable when the input parameters change [29]. This is a complete new approach to the analysis of blood glucose time series, where most of the methods have been based on DFA [30,31] or Sample Entropy (Multiscale) [32,33,21].…”

Nonlinear correlations in multifractals: Visibility graphs of magnitude and sign series

“…In this article, we apply the horizontal visibility graph algorithm to map fractal and multifratal time series into graphs. By investigating topological characteristics of the resulting graphs, we first show that this approach can well detect linear and nonlinear correlations, even for situations that DFA and MFDFA predict uncorrelatedness, due to some technical issues [23,29,30]. On the other hand, we show that owing to the unique characterisitc of the horizontal visibility graph algorithm, one can calculate linear or nonlinear correlations, without the need to eliminate the impact of non-Gaussianity of the original series.…”

“…In DFA and MFDFA techniques, one usually confronts with some challenges such as choosing an appropriate polynomial order for detrending procedure, finding a proper scaling region, and detecting correct correlations that can be affected by the probability distribution function (PDF) of the series. Recently, it has been shown that in some conditions, DFA and MFDFA are not able to extract correct scaling behaviors of a time series [23,29,30]. The existence of crossovers in the scaling behavior at some particular scale s c along with the q dependency of that s c are two examples of possible inaccuracy in the multifractal spectrum estimation.…”

On the Validity of Detrended Fluctuation Analysis at Short Scales

“…FFM has become the standard method to create a controlled power-law correlated time series, and it is used in many contexts for that purpose [ 21 , 22 , 23 , 24 , 25 , 26 ]…”