Don't bleach chaotic data

TL;DR

Bleaching time series data by removing linear correlations can obscure the underlying chaotic structure, leading to misleading results in nonlinear analysis, despite its theoretical appeal for avoiding spurious invariants.

Contribution

The paper demonstrates that bleaching chaotic data can hide deterministic structures, challenging its use in nonlinear time series analysis.

Findings

Bleaching obscures the deterministic structure of chaotic data.

Nonchaotic data are less affected by bleaching.

Numerical experiments show the adverse effects of bleaching on chaos detection.

Abstract

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.