Detecting nonlinearity in multivariate time series

TL;DR

This paper introduces a new method for detecting nonlinearity in multivariate time series by combining linear redundancy analysis with surrogate data techniques, applicable to various dependence structures.

Contribution

It extends existing nonlinearity tests to multivariate data, allowing for specific dependence structure analysis and reducing false positives from surrogate data limitations.

Findings

Successfully tested on simulated linear and nonlinear series

Applied to meteorology and physiology data

Improves reliability of nonlinearity detection in multivariate series

Abstract

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 avoid spurious 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.