# Regularized Estimation of High-dimensional Factor-Augmented Vector Autoregressive (FAVAR) Models

Lin, J., & Michailidis, G. (2020). Regularized Estimation of High-dimensional Factor-Augmented Vector Autoregressive (FAVAR) Models. The Journal of Machine Learning Research, Volume 21

44 Pages Posted: 24 Jun 2020

See all articles by Jiahe Lin

## Jiahe Lin

University of Michigan at Ann Arbor

## George Michailidis

University of Michigan at Ann Arbor

Date Written: March 1, 2018

### Abstract

A factor-augmented vector auto-regressive (FAVAR) model is defined by a VAR equation that captures lead-lag correlations among a set of observed variables X and latent factors F, and a calibration equation that relates another set of observed variables Y with F and X. The latter equation is used to estimate the factors that are subsequently used in estimating the parameters of the VAR system. The FAVAR model has become popular in applied economic research, since it can summarize a large number of variables of interest as a few factors through the calibration equation and subsequently examine their influence on core variables of primary interest through the VAR equation. However, there is increasing need for examining lead-lag relationships between a large number of time series, while incorporating information from another high-dimensional set of variables. Hence, in this paper we investigate the FAVAR model under high-dimensional scaling. We introduce an appropriate identification constraint for the model parameters, which when incorporated into the formulated optimization problem yields estimates with good statistical properties. Further, we address a number of technical challenges introduced by the fact that estimates of the VAR system model parameters are based on estimated rather than directly observed quantities. The performance of the proposed estimators is evaluated on synthetic data. Further, the model is applied to commodity prices and reveals interesting and interpret-able relationships between the prices and the factors extracted from a set of global macroeconomic indicators.

Keywords: Model Identifiability, Compactness, Low-Rank Plus Sparse Decomposition, Finite-Sample Bounds

JEL Classification: C10, C13, C32

Suggested Citation

Lin, Jiahe and Michailidis, George, Regularized Estimation of High-dimensional Factor-Augmented Vector Autoregressive (FAVAR) Models (March 1, 2018). Lin, J., & Michailidis, G. (2020). Regularized Estimation of High-dimensional Factor-Augmented Vector Autoregressive (FAVAR) Models. The Journal of Machine Learning Research, Volume 21, Available at SSRN: https://ssrn.com/abstract=3615069 or http://dx.doi.org/10.2139/ssrn.3615069

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