  Multilayer networks proved to be suitable in extracting and providing
dependency information of different complex systems. The construction of these
networks is difficult and is mostly done with a static approach, neglecting
time delayed interdependences. Tensors are objects that naturally represent
multilayer networks and in this paper, we propose a new methodology based on
Tucker tensor autoregression in order to build a multilayer network directly
from data. This methodology captures within and between connections across
layers and makes use of a filtering procedure to extract relevant information
and improve visualization. We show the application of this methodology to
different stationary fractionally differenced financial data. We argue that our
result is useful to understand the dependencies across three different aspects
of financial risk, namely market risk, liquidity risk, and volatility risk.
Indeed, we show how the resulting visualization is a useful tool for risk
managers depicting dependency asymmetries between different risk factors and
accounting for delayed cross dependencies. The constructed multilayer network
shows a strong interconnection between the volumes and prices layers across all
the stocks considered while a lower number of interconnections between the
uncertainty measures is identified.
