  The key feature for the successful implementation of the surrogate data test
for nonlinearity on a scalar time series is the generation of surrogate data
that represent exactly the null hypothesis (statically transformed normal
stochastic process), i.e. they possess the sample autocorrelation and amplitude
distribution of the given data. A new conceptual approach and algorithm for the
generation of surrogate data is proposed, called {\em statically transformed
  autoregressive process} (STAP). It identifies a normal autoregressive process
and a monotonic static transform, so that the transformed realisations of this
process fulfill exactly both conditions and do not suffer from bias in
autocorrelation as the surrogate data generated by other algorithms. The
appropriateness of STAP is demonstrated with simulated and real world data.
