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The Fixed-b Limiting Distribution and the ERP of HAR Tests Under Nonstationarity

Alessandro Casini

arXiv 29 Nov 2021 · Econometrics · publishedJournal of Econometrics (2023) · 3 citations (OpenAlex)

arXiv:2111.14590 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We show that the nonstandard limiting distribution of HAR test statistics under fixed-b asymptotics is not pivotal (even after studentization) when the data are nonstationarity. It takes the form of a complicated function of Gaussian processes and depends on the integrated local long-run variance and on on the second moments of the relevant series (e.g., of the regressors and errors for the case of the linear regression model). Hence, existing fixed-b inference methods based on stationarity are not theoretically valid in general. The nuisance parameters entering the fixed-b limiting distribution can be consistently estimated under small-b asymptotics but only with nonparametric rate of convergence. Hence, We show that the error in rejection probability (ERP) is an order of magnitude larger than that under stationarity and is also larger than that of HAR tests based on HAC estimators under conventional asymptotics. These theoretical results reconcile with recent finite-sample evidence in Casini (2021) and Casini, Deng and Perron (2021) who showing that fixed-b HAR tests can perform poorly when the data are nonstationary. They can be conservative under the null hypothesis and have non-monotonic power under the alternative hypothesis irrespective of how large the sample size is.

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32
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Jansson, M (2004) The error in rejection probability of simple autocorrelation robust tests1.00083100%
2Kiefer, N.M., Vogelsang, T.J (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests1.00083100%
3Casini, A., Deng, T., Perron, P (2023) Theory of low frequency contamination from nonstationarity and misspecification: consequences for HAR inference self0.9507486%
4Casini, A (2023) Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstati… self0.94112583%
5Sun, Y., Phillips, P.C.B., Jin, S (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing0.87418467%
6Andrews, D.W.K (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation0.84333100%
7Lazarus, E., Lewis, D.J., Stock, J.H (2021) The size-power tradeoff in HAR inference0.84333100%
8Kiefer, N.M., Vogelsang, T.J (2002) Heteroskedasticity-autocorrelation robust standard errors using the Bartlett kernel without truncation0.81142100%
9Kiefer, N.M., Vogelsang, T.J (2002) Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal to Sample Size0.7373367%
10Kiefer, N.M., Vogelsang, T.J., Bunzel, H (2000) Simple robust testing of regression hypotheses0.73732100%

Showing the top 10 of 32 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference1.00063
2Prewhitened Long-Run Variance Estimation Robust to Nonstationarity0.40511
3Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models0.40511
4A general randomized test for Alpha0.40511