Constrained Randomisation of Time Series for Nonlinearity Tests

We discuss the problem of generating time sequences that fulfil given constraints but are random otherwise. This is an important ingredient for generalised nonlinearity tests which make use of Monte Carlo resampling. We briefly discuss standard methods available for a limited range of problems. Then we put forth a novel scheme in which one can define arbitrary sets of observables and test if these observables give a complete account of the serial correlation structure in the data. The most immediate application is the detection of correlations beyond the two-point auto-covariance, even in a non-Gaussian setting. More general constraints, also including multivariate, nonlinear, and non-stationary properties, can be implemented in the form of a cost function to be minimised. 1 Introduction In the statistical evaluation of empirical observations, randomisation of data is an important means to obtain probability distributions and confidence intervals in cases where assumptions on the norm..