  Current tests for nonlinearity compare a time series to the null hypothesis
of a Gaussian linear stochastic process. For this restricted null assumption,
random surrogates can be constructed which are constrained by the linear
properties of the data. We propose a more general null hypothesis allowing for
nonlinear rescalings of a Gaussian linear process. We show that such rescalings
cannot be accounted for by a simple amplitude adjustment of the surrogates
which leads to spurious detection of nonlinearity. An iterative algorithm is
proposed to make appropriate surrogates which have the same autocorrelations as
the data and the same probability distribution.
