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THEORY OF LOW FREQUENCY CONTAMINATION FROM NONSTATIONARITY AND MISSPECIFICATION: CONSEQUENCES FOR HAR INFERENCE

Published online by Cambridge University Press:  27 December 2024

Alessandro Casini Open the ORCID record for Alessandro Casini [Opens in a new window] ,
Taosong Deng Open the ORCID record for Taosong Deng [Opens in a new window]  and
Pierre Perron
Alessandro Casini*
Affiliation:
University of Rome Tor Vergata
Taosong Deng*
Affiliation:
Hunan University
Pierre Perron*
Affiliation:
Boston University
*
Corresponding author at: Dep. of Economics and Finance, University of Rome Tor Vergata, Via Columbia 2, Rome, 00133, IT.; e-mail: alessandro.casini@uniroma2.it. College of Finance and Statistics, Hunan University, 109 Shijiachong Road, Yuelu District, Changsha, Hunan 41006, China. e-mail: tsdeng@hnu.edu.cn. Dep. of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, US. e-mail: perron@bu.edu.
Corresponding author at: Dep. of Economics and Finance, University of Rome Tor Vergata, Via Columbia 2, Rome, 00133, IT.; e-mail: alessandro.casini@uniroma2.it. College of Finance and Statistics, Hunan University, 109 Shijiachong Road, Yuelu District, Changsha, Hunan 41006, China. e-mail: tsdeng@hnu.edu.cn. Dep. of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, US. e-mail: perron@bu.edu.
Corresponding author at: Dep. of Economics and Finance, University of Rome Tor Vergata, Via Columbia 2, Rome, 00133, IT.; e-mail: alessandro.casini@uniroma2.it. College of Finance and Statistics, Hunan University, 109 Shijiachong Road, Yuelu District, Changsha, Hunan 41006, China. e-mail: tsdeng@hnu.edu.cn. Dep. of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, US. e-mail: perron@bu.edu.
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Abstract

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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 show theoretically that nonparametric smoothing over time is robust to low frequency contamination. Nonstationarity can have consequences for both the size and power of HAR tests. Under the null hypothesis there are larger size distortions than when data are stationary. Under the alternative hypothesis, existing LRV estimators tend to be inflated and HAR tests can 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 suffer from this problem. 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 regression model. The results show that the distortions in the rejection rates can be induced by time variation in the second moments even when there is no break in the mean.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 42
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

We are grateful to Peter C.B. Phillips, Anna Mikusheva and the referees for useful suggestions. We thank Whitney Newey and Tim Vogelsang for discussions and Andrew Chesher, Adam McCloskey, Zhongjun Qu, and Daniel Whilem for comments.

References

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