# DeepVARwT: Deep Learning for a VAR Model with Trend

arXiv: https://arxiv.org/abs/2209.10587 · HTML: https://mlsanity.com/paper/2209.10587/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [High-dimensional vector autoregressive time series modeling via tensor decomposition](https://mlsanity.com/paper/1909.06624/) (2019)
- [Enforcing stationarity through the prior in vector autoregressions](https://mlsanity.com/paper/2004.09455/) (2020)

## Abstract (arXiv)

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.