DeepVARwT: Deep Learning for a VAR Model with Trend

TL;DR

DeepVARwT introduces a deep learning-based method using LSTM networks to jointly estimate trends and dependencies in multivariate time series, improving over traditional detrending approaches.

Contribution

It develops a novel deep learning framework for simultaneous trend estimation and VAR modeling, ensuring model stability and causality.

Findings

Outperforms existing models in prediction accuracy on real data

Accurately estimates complex trend functions in simulations

Demonstrates stability and causality enforcement in the proposed method

Abstract

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.