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The vector autoregressive (VAR) model has been used to describe thedependence within and across multiple time series. This is a model forstationary time series which can be extended to allow the presence of adeterministic trend in each series. Detrending the data either parametricallyor nonparametrically before fitting the VAR model gives rise to more errors inthe latter part. In this study, we propose a new approach called DeepVARwT thatemploys deep learning methodology for maximum likelihood estimation of thetrend 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 thetransformation of Ansley & Kohn (1986). We provide a simulation study and anapplication to real data. In the simulation study, we use realistic trendfunctions generated from real data and compare the estimates with truefunction/parameter values. In the real data application, we compare theprediction performance of this model with state-of-the-art models in theliterature.

DeepVARwT: Deep Learning for a VAR Model with Trend