Ridge Regularized Estimation of VAR Models for Inference

TL;DR

This paper investigates ridge regression for VAR model estimation, analyzing its properties, comparing it with Bayesian methods, and evaluating impulse response estimation through simulations.

Contribution

It provides a comprehensive analysis of ridge regression in VAR models, including asymptotic properties, cross-validation, and comparison with other methods.

Findings

Ridge regression offers effective regularization for VAR models.

Asymptotic distribution of estimators is characterized.

Ridge regression performs competitively in impulse response estimation.

Abstract

Ridge regression is a popular method for dense least squares regularization. In this work, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed and a comparison is made with Bayesian ridge-type estimators. The asymptotic distribution and the properties of cross-validation techniques are analyzed. Finally, the estimation of impulse response functions is evaluated with Monte Carlo simulations and ridge regression is compared with a number of similar and competing methods.