Prewhitened Long-Run Variance Estimation Robust to Nonstationarity

TL;DR

This paper proposes a new nonparametric nonlinear VAR prewhitened long-run variance estimator that remains robust under nonstationarity, improving hypothesis testing accuracy in various models.

Contribution

It introduces a novel LRV estimator explicitly accounting for nonstationarity, with sharper MSE bounds and data-dependent bandwidth selection.

Findings

Estimator is robust to nonstationarity and heteroskedasticity.

Achieves accurate null rejection rates and good power.

Provides sharper MSE bounds for LRV estimation.

Abstract

We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite-sample properties under nonstationarity (i.e., fixed-b methods), or are theoretically valid under the null hypothesis but lead to tests that are not consistent under nonstationary alternative hypothesis (i.e., both fixed-b and traditional HAC estimators). The proposed estimator accounts explicitly for nonstationarity, unlike previous prewhitened procedures which are known to be unreliable, and leads to tests with accurate null rejection rates and good monotonic power. We also establish MSE bounds for LRV estimation that are sharper than previously established and use them to determine the data-dependent bandwidths.