  Understanding the properties of time-indexed multivariate data has been a
predominant topic mainly to address open issues in multivariate time series
analysis. Usually, the methodologies used to analyze multivariate time series
are based on adapting approaches for univariate settings or on assumptions and
parameters for specific problems. A different strategy uses complex network to
obtain an additional and reduced representation of temporal and causal
properties of the time series data. Recent strategies involve mapping
multivariate time series into high-level network structures, specifically into
multiplex networks representing interconnections between contemporary
timestamps of different time series components. In this work, we propose a new
mapping method that takes advantage of the entire structure of multilayer
networks. We introduce the multilayer horizontal visibility graph that is based
on the new concept of cross-horizontal visibility between lagged timestamps of
different components, which allows describing the cross-dimension dependencies
via inter-layer edges. We use a set of existing topological measures of
multilayer networks as well as a novel measure to evaluate and validate our
approach, which is parameter-free, does not require data pre-processing and is
applicable to any kind of multivariate time series data. We provide an
extensive experimental evaluation, where we explore the proposed topological
measures, showing that the inter-layer edges based on cross-horizontal
visibility preserve more information about the time series data after the
mappings, information that would inevitably be lost using mapping methods that
result in single-layer and multiplex structures. We also verify that the
information mapped by the inter-layer edges is not enough on its own, but that
it complements the data information captured by the commonly used intra-layer
edges.
