Detecting Nonlinearity in Data with Long Coherence Times

Details Detecting Nonlinearity in Data with Long Coherence Times Detecting Nonlinearity in Data with Long Coherence Times

1993-02-26

arxiv.org/abs/comp-gas/9302003v2

Nonlinear Sciences

Cellular Automata and Lattice Gases

26 pages, Postscript, includes figures embedded in text. This version fixes a very old postscript bug which prevented the pape

Scientific paper

We consider the limitations of two techniques for detecting nonlinearity in time series. The first technique compares the original time series to an ensemble of surrogate time series that are constructed to mimic the linear properties of the original. The second technique compares the forecasting error of linear and nonlinear predictors. Both techniques are found to be problematic when the data has a long coherence time; they tend to indicate nonlinearity even for linear time series. We investigate the causes of these difficulties both analytically and with numerical experiments on ``real'' and computer-generated data. In particular, although we do see some initial evidence for nonlinear structure in the SFI dataset E, we are inclined to dismiss this evidence as an artifact of the long coherence time.

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