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Alternative HAC covariance matrix estimators with improved finite sample properties

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  • Hartigan, Luke

Abstract

HAC estimators are known to produce test statistics that reject too frequently in finite samples. One neglected reason comes from the OLS residuals used to construct the HAC estimator. If the design matrix contains leverage points, such as from outliers, then the OLS residuals will be downward biased. This makes the OLS residuals smaller than otherwise, thereby reducing their variance. Transformations to offset the bias via inflating the OLS residuals have been available in the related HC literature for some time, but these have been overlooked so far in the HAC literature. Using HC-inspired techniques and a range of simulations, this paper provides strong support for replacing the OLS residual-based HAC estimator with two new alternatives called HAC-PE and HAC-MDE when estimating coefficient standard errors to produce test statistics because they display much less size distortion in practice.

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  • Hartigan, Luke, 2018. "Alternative HAC covariance matrix estimators with improved finite sample properties," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 55-73.
    • Handle: RePEc:eee:csdana:v:119:y:2018:i:c:p:55-73
    DOI: 10.1016/j.csda.2017.09.007
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    Cited by:

    1. Luke Hartigan & James Morley, 2020. "A Factor Model Analysis of the Australian Economy and the Effects of Inflation Targeting," The Economic Record, The Economic Society of Australia, vol. 96(314), pages 271-293, September.
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    3. Luke Hartigan & Michelle Wright, 2023. "Monitoring Financial Conditions and Downside Risk to Economic Activity in Australia," The Economic Record, The Economic Society of Australia, vol. 99(325), pages 253-287, June.
    4. Luke Hartigan, 2016. "Testing for Symmetry in Weakly Dependent Time Series," Discussion Papers 2016-18, School of Economics, The University of New South Wales.

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    More about this item

    Keywords

    Covariance matrix estimation; Finite sample analysis; Leverage points; Hypothesis testing; Monte Carlo simulation; Inference;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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