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Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference

Alessandro Casini, Taosong Deng, Pierre Perron

arXiv 2 Mar 2021 · Econometrics · publishedEconometric Theory (2024) · 11 citations (OpenAlex)

arXiv:2103.01604 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We establish theoretical results about the low frequency contamination (i.e., long memory effects) induced by general nonstationarity for estimates such as the sample autocovariance and the periodogram, and deduce consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We present explicit expressions for the asymptotic bias of these estimates. We distinguish cases where this contamination only occurs as a small-sample problem and cases where the contamination continues to hold asymptotically. We show theoretically that nonparametric smoothing over time is robust to low frequency contamination. Our results provide new insights on the debate between consistent versus inconsistent long-run variance (LRV) estimation. Existing LRV estimators tend to be in inflated when the data are nonstationary. This results in HAR tests that can be undersized and exhibit dramatic power losses. Our theory indicates that long bandwidths or fixed-b HAR tests suffer more from low frequency contamination relative to HAR tests based on HAC estimators, whereas recently introduced double kernel HAC estimators do not super from this problem. Finally, we present second-order Edgeworth expansions under nonstationarity about the distribution of HAC and DK-HAC estimators and about the corresponding t-test in the linear regression model.

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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
1Casini, A (2024) The fixed-b limiting distribution and the ERP of HAR tests under nonstationarity self1.00063100%
2Andrews, D.W.K (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation0.97325592%
3Casini, A (2023) Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstati… self0.95616788%
4Newey, W.K., West, K.D (1987) A simple positive semidefinite, heteroskedastic and autocorrelation consistent covariance matrix0.874162100%
5Jansson, M (2004) The error in rejection probability of simple autocorrelation robust tests0.81142100%
6Lazarus, E., Lewis, D.J., Stock, J.H., Watson, M.W (2018) HAR inference: recommendations for practice0.81142100%
7Sun, Y., Phillips, P.C.B., Jin, S (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing0.81142100%
8Velasco, C., Robinson, P.M (2001) Edgeworth expansions for spectral density estimates and studentized sample mean0.76318344%
9Bentkus, R.Y., Rudzkis, R.A (1982) On the distribution of some statistical estimates of spectral density0.7373367%
10Mikosch, T., Starica, C (2004) Nonstationarities in financial time series, the long-range dependence, and the IGARCH effects0.7373367%

Showing the top 10 of 102 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 Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models1.00073
2The Fixed-$b$ Limiting Distribution and the ERP of HAR Tests Under Nonstationarity0.95074
3Prewhitened Long-Run Variance Estimation Robust to Nonstationarity0.72183
4Change-Point Analysis of Time Series with Evolutionary Spectra0.40511