Reduced-Rank Covariance Estimation in Vector Autoregressive Modeling

TL;DR

This paper introduces a reduced-rank covariance estimator for large-dimensional VAR models, improving estimation accuracy and interpretability over traditional methods, with demonstrated benefits in simulation and real data applications.

Contribution

The paper develops a novel reduced-rank covariance estimator for VAR models, integrating it into model fitting procedures and showing improved performance and interpretability.

Findings

Outperforms competing covariance estimators in simulations

Enhances model fitting and forecasting accuracy

Provides interpretable dependence structures in VAR models

Abstract

We consider reduced-rank modeling of the white noise covariance matrix in a large dimensional vector autoregressive (VAR) model. We first propose the reduced-rank covariance estimator under the setting where independent observations are available. We derive the reduced-rank estimator based on a latent variable model for the vector observation and give the analytical form of its maximum likelihood estimate. Simulation results show that the reduced-rank covariance estimator outperforms two competing covariance estimators for estimating large dimensional covariance matrices from independent observations. Then we describe how to integrate the proposed reduced-rank estimator into the fitting of large dimensional VAR models, where we consider two scenarios that require different model fitting procedures. In the VAR modeling context, our reduced-rank covariance estimator not only provides interpretable descriptions of the dependence structure of VAR processes but also leads to improvement in model-fitting and forecasting over unrestricted covariance estimators. Two real data examples are presented to illustrate these fitting procedures.