Don't bleach chaotic data.
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.
Theiler
James
J
Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545;Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, New Mexico 87501Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, New Mexico 87501Prediction Company, 320 Aztec Street, Santa Fe, New Mexico 87501.
Eubank
Stephen
S