  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.
