https://doi.org/10.1140/epjp/s13360-020-00980-x
Regular Article
Extended detrended fluctuation analysis: effects of nonstationarity and application to sleep data
1
Saratov State University, Astrakhanskaya 83, 410012, Saratov, Russia
2
Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies”, 23 Gagarina Avenue, 603950, Nizhny Novgorod, Russia
3
Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473, Potsdam, Germany
4
Institute of Physics, Humboldt University Berlin, 12489, Berlin, Germany
Received:
11
October
2020
Accepted:
30
November
2020
Published online:
2
January
2021
Extended detrended fluctuation analysis (EDFA) is a recently proposed modification of the conventional method, which provides a characterization of complex time series with varying nonstationarity. It evaluates two scaling exponents for a better quantification of inhomogeneous datasets. Here, we study the effect of different types of nonstationarity on these exponents, including trend, switching between processes with distinct statistical properties and energy variability. Using the simulated signals, we show that the first two types of nonstationarity have the strongest effect for anticorrelated processes and complicate their diagnosis. Nonstationarity in energy is more crucial for time series with positive long-range correlations. Next, we apply EDFA to rat experiments to study the activation of brain lymphatic drainage during sleep. Our analysis reveals significant distinctions in EDFA’s measures between the background electrical activity of the brain and the stage of sleep. The latter offers an indirect way to identify and characterize the nightly activation of the drainage and clearance of brain tissue.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
