  The vector autoregressive (VAR) model has been used to describe the
dependence within and across multiple time series. This is a model for
stationary time series which can be extended to allow the presence of a
deterministic trend in each series. Detrending the data either parametrically
or nonparametrically before fitting the VAR model gives rise to more errors in
the latter part. In this study, we propose a new approach called DeepVARwT that
employs deep learning methodology for maximum likelihood estimation of the
trend and the dependence structure at the same time. A Long Short-Term Memory
(LSTM) network is used for this purpose. To ensure the stability of the model,
we enforce the causality condition on the autoregressive coefficients using the
transformation of Ansley & Kohn (1986). We provide a simulation study and an
application to real data. In the simulation study, we use realistic trend
functions generated from real data and compare the estimates with true
function/parameter values. In the real data application, we compare the
prediction performance of this model with state-of-the-art models in the
literature.
