Volume 12 Supplement 1
Adaptive time-varying detrended fluctuations analysis: a new method for characterizing time-varying scaling parameters in physiological time series
© Berthouze and Farmer; licensee BioMed Central Ltd. 2011
Published: 18 July 2011
Detrended fluctuations analysis (DFA)  is a technique commonly used to assess the presence of long-range temporal correlations (LRTCs) in physiological time series. The method is based on assessing the parameters of the linear regression in the loglog space of the residuals of the detrended signal over different box sizes; providing an estimate of the Hurst exponent. Convergence of the method is asymptotic only  and therefore its application requires lengthy time series assuming a stationary scaling exponent. Methods for dealing with nonstationarities due to, e.g., data manipulation (e.g., stitching), addition of random outliers or the presence of different standard deviations or correlations assume the superposition of independent processes and rely on a graphical interpretation of changes in the slope of the residuals at various box sizes . However, most neurophysiological experiments involve a task or neurophysiological perturbations. These may disrupt the LRTCs in unexpected and interesting ways. It is therefore of importance to devise a robust method for tracking changes in the parameter that best characterizes LRTCs.
We derived analytical formulations for the bias and variance of the error committed when using the scaling exponent obtained by DFA on a given time-series to predict the scaling exponent of the same time-series but shifted by one sample (assuming the scaling exponent is stationary at a very short time scale). These results make it possible to define a Kalman filter for tracking fluctuations in scaling exponents over a longer time scale. Estimates for the measurement noise of the filter are obtained by pooling DFA estimates of the signal across a small number of time shifts. Robust estimates of the state vector are obtained by augmenting the filter with a smoothing procedure.
- Peng C-K, Havlin S, Stanley HE, Goldberger AL: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 1995, 5: 82-87. 10.1063/1.166141.View ArticlePubMedGoogle Scholar
- Bardet J, Kammoun I: Asymptotic properties of the detrended fluctuation analysis of long-range-dependent processes. IEEE Trans Inf Theory. 2008, 54 (5): 2041-2052. 10.1109/TIT.2008.920328.View ArticleGoogle Scholar
- Chen Z, Ivanov PC, Hu K, Stanley HE: Effect of nonstationarities on detrended fluctuation analysis. Phys Rev E. 2002, 65: 041107-10.1103/PhysRevE.65.041107.View ArticleGoogle Scholar
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