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Detecting nonlinearity in multivariate time series

Milan Palus
Santa Fe Institute, 1399 Hyde Park Road
Santa Fe, NM 87501, USA; and
Institute of Computer Science, Academy of Sciences of the Czech Republic
Pod vodárenskou vezí 2, 182 07 Prague 8, Czech Republic


We propose an extension to time series with several simultaneously measured variables of the nonlinearity test, which combines the redundancy -- linear redundancy approach with the surrogate data technique. For several variables various types of the redundancies can be defined, in order to test specific dependence structures between/among (groups of) variables. The null hypothesis of a multivariate linear stochastic process is tested using the multivariate surrogate data. The linear redundancies are used in order to avoidspurious results due to imperfect surrogates. The method is demonstrated using two types of numerically generated multivariate series (linear and nonlinear) and experimental multivariate data from meteorology and physiology.

Phys. Lett. A 213 (1996) 138-147

Milan Palus
January 1997