  The method of surrogate data is a tool to test whether data were generated by
some class of model. Tests based on the periodogram have been proposed to
decide if linear systems driven by Gaussian noise could have generated a sample
time series. We show that this procedure based on the periodogram, in general,
misspecifies the test statistic. Based on the theory of linear systems we
suggest an alternative procedure to obtain the correct distribution of the test
statistic and discuss problems of this approach.
