A Unified Frequency Domain Cross-Validatory Approach to HAC Standard Error Estimation

TL;DR

This paper introduces a unified frequency domain cross-validation method for HAC standard error estimation, allowing simultaneous model and parameter selection for both parametric and nonparametric spectral estimators, demonstrating improved reliability over existing methods.

Contribution

It proposes a novel FDCV approach that unifies model selection for various spectral estimators, including REML autoregressive and lag-weights with Parzen kernel, with an efficient computation technique.

Findings

FDCV compares favorably with Andrews-Monahan and Newey-West estimators.

The method demonstrates high reliability through simulation studies.

It enables simultaneous tuning parameter selection for diverse spectral estimators.

Abstract

A unified frequency domain cross-validation (FDCV) method is proposed to obtain a heteroskedasticity and autocorrelation consistent (HAC) standard error. This method enables model/tuning parameter selection across both parametric and nonparametric spectral estimators simultaneously. The candidate class for this approach consists of restricted maximum likelihood-based (REML) autoregressive spectral estimators and lag-weights estimators with the Parzen kernel. Additionally, an efficient technique for computing the REML estimators of autoregressive models is provided. Through simulations, the reliability of the FDCV method is demonstrated, comparing favorably with popular HAC estimators such as Andrews-Monahan and Newey-West.