# High dimensional VAR with low rank transition

## TL;DR

This paper introduces a low-rank constrained VAR model tailored for high-dimensional, highly correlated time series, demonstrating superior prediction accuracy especially in high-dimensional macroeconomic datasets.

## Contribution

It develops a novel low-rank VAR model with methods for estimation, prediction, and rank selection, applicable to high-dimensional series with hidden factors.

## Key findings

- Excellent performance on simulated datasets
- Competitive with state-of-the-art in small dimensions
- Improves prediction in high-dimensional macroeconomic data

## Abstract

We propose a vector auto-regressive (VAR) model with a low-rank constraint on the transition matrix. This new model is well suited to predict high-dimensional series that are highly correlated, or that are driven by a small number of hidden factors. We study estimation, prediction, and rank selection for this model in a very general setting. Our method shows excellent performances on a wide variety of simulated datasets. On macro-economic data from Giannone et al. (2015), our method is competitive with state-of-the-art methods in small dimension, and even improves on them in high dimension.