Inference in Non-stationary High-Dimensional VARs

TL;DR

This paper develops a robust inferential method for testing Granger causality in high-dimensional, non-stationary VAR models that does not require prior knowledge of the series' integration order.

Contribution

It introduces a lag augmentation approach combined with a variable selection procedure, enabling valid inference in high-dimensional, non-stationary settings without knowing the integration order.

Findings

Method performs well in finite sample simulations.

Application demonstrates importance of accounting for unknown integration orders.

Approach effectively identifies causal relationships in economic data.

Abstract

In this paper we construct an inferential procedure for Granger causality in high-dimensional non-stationary vector autoregressive (VAR) models. Our method does not require knowledge of the order of integration of the time series under consideration. We augment the VAR with at least as many lags as the suspected maximum order of integration, an approach which has been proven to be robust against the presence of unit roots in low dimensions. We prove that we can restrict the augmentation to only the variables of interest for the testing, thereby making the approach suitable for high dimensions. We combine this lag augmentation with a post-double-selection procedure in which a set of initial penalized regressions is performed to select the relevant variables for both the Granger causing and caused variables. We then establish uniform asymptotic normality of a second-stage regression involving only the selected variables. Finite sample simulations show good performance, an application to investigate the (predictive) causes and effects of economic uncertainty illustrates the need to allow for unknown orders of integration.