Ridge Regularized Estimation of VAR Models for Inference

Ridge regression is a popular regularization method that has wide applicability, as many regression problems can be cast in this form. However, ridge is only seldom applied in the estimation of vector autoregressive models -- even though ridge naturally arises in Bayesian time series modeling. In this work I study ridge regression in the context of vector autoregressive process estimation and inference. The effects of shrinkage are analyzed and asymptotic theory is derived enabling inference. Frequentist and Bayesian ridge approaches are compared, and a hybrid VAR-LP estimator is proposed. 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.