  Our understanding of a variety of phenomena in physics, biology and economics
crucially depends on the analysis of multivariate time series. While a wide
range of tools and techniques for time series analysis already exist, the
increasing availability of massive data structures calls for new approaches for
multidimensional signal processing. We present here a non-parametric method to
analyse multivariate time series, based on the mapping of a multidimensional
time series into a multilayer network, which allows to extract information on a
high dimensional dynamical system through the analysis of the structure of the
associated multiplex network. The method is simple to implement, general,
scalable, does not require ad hoc phase space partitioning, and is thus
suitable for the analysis of large, heterogeneous and non-stationary time
series. We show that simple structural descriptors of the associated multiplex
networks allow to extract and quantify nontrivial properties of coupled chaotic
maps, including the transition between different dynamical phases and the onset
of various types of synchronization. As a concrete example we then study
financial time series, showing that a multiplex network analysis can
efficiently discriminate crises from periods of financial stability, where
standard methods based on time-series symbolization often fail.
