Abstract
We discuss the problem of generating time sequences that fulfill given constraints but are random otherwise. This is an important ingredient for generalized nonlinearity tests that use 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 autocovariance, even in a non-Gaussian setting. More general constraints, also including multivariate, nonlinear, and nonstationary properties, can be implemented in the form of a cost function to be minimized.
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Schreiber, T., Schmitz, A. (2001). Constrained Randomization of Time Series for Nonlinearity Tests. In: Mees, A.I. (eds) Nonlinear Dynamics and Statistics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0177-9_8
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DOI: https://doi.org/10.1007/978-1-4612-0177-9_8
Publisher Name: Birkhäuser, Boston, MA
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