DeepVARwT: deep learning for a VAR model with trend

Time series modelling and prediction is useful in many fields of application such as economics, finance and engineering. 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. In this paper, we demonstrate a new approach 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. We provide a simulation study and applications to real data. In the simulation study, we use realistic trend functions estimated from real data and compare the estimates with true function/parameter values. In the real data applications, we compare the prediction performance of this model with state-of-the-art models in the literature.