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HAC Corrections for Strongly Autocorrelated Time Series

Ulrich K. Müller

Journal of Business & Economic Statistics, 2014, vol. 32, issue 3, 311-322

Abstract: 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.

Date: 2014
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DOI: 10.1080/07350015.2014.931238

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