HAC Corrections for Strongly Autocorrelated Time Series

• Published in: Journal of business & economic statistics Vol. 32; no. 3; pp. 311 - 322
• Main Author: Müller, Ulrich K.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03-07-2014; American Statistical Association; Taylor & Francis Ltd
• Subjects: Approximation; Autocorrelation; Consistent estimators; Correlation analysis; Critical values; Density estimation; Estimators; Failure analysis; Inference; Local-to-unity; Long-run variance; Normal distribution; Spectral energy distribution; Statistical inference; Studies; Time series; Weighted averages
• ISSN: 0735-0015; 1537-2707
• DOI: 10.1080/07350015.2014.931238

Applied work routinely relies on heteroscedasticity and autocorrelation consistent (HAC) standard errors when conducting inference in a time series setting. As is well known, however, these corrections perform poorly in small samples under pronounced autocorrelations. In this article, I first provide a review of popular methods to clarify the reasons for this failure. I then derive inference that remains valid under a specific form of strong dependence. In particular, I assume that the long-run properties can be approximated by a stationary Gaussian AR(1) model, with coefficient arbitrarily close to one. In this setting, I derive tests that come close to maximizing a weighted average power criterion. Small sample simulations show these tests to perform well, also in a regression context.