Statically Transformed Autoregressive Process and Surrogate Data Test for Nonlinearity

Abstract

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.