The fixed-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg" display="inline" id="d1e650"><mml:mi mathvariant="bold-italic">b</mml:mi></mml:math> limiting distribution and the ERP of HAR tests under nonstationarity

Casini, Alessandro

doi:10.1016/j.jeconom.2023.105625

Journal of Econometrics

2024

DOI: 10.1016/j.jeconom.2023.105625

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The fixed-b limiting distribution and the ERP of HAR tests under nonstationarity

Alessandro Casini

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2024

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Cited by 2 publications

References 29 publications

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Prewhitened long-run variance estimation robust to nonstationarity

Casini,

Perron

2024

Journal of Econometrics

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Prewhitened long-run variance estimation robust to nonstationarity

Casini,

Perron

2024

Journal of Econometrics

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Theory of Low Frequency Contamination From Nonstationarity and Misspecification: Consequences for Har Inference

Casini,

Deng,

Perron

2024

Econom. Theory

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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.

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The fixed-b limiting distribution and the ERP of HAR tests under nonstationarity

Cited by 2 publications

References 29 publications

Prewhitened long-run variance estimation robust to nonstationarity

Prewhitened long-run variance estimation robust to nonstationarity

Theory of Low Frequency Contamination From Nonstationarity and Misspecification: Consequences for Har Inference

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