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Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models

Alessandro Casini

arXiv 4 Mar 2021 · Econometrics · publishedJournal of Econometrics (2022) · 17 citations (OpenAlex)

arXiv:2103.02981 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We develop a theory of evolutionary spectra for heteroskedasticity and autocorrelation robust (HAR) inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic time series which may arise either from parameter variation or model misspecification. In such a context, the theories that support HAR inference are either not applicable or do not provide accurate approximations. HAR tests standardized by existing long-run variance estimators then may display size distortions and little or no power. This issue can be more severe for methods that use long bandwidths (i.e., fixed-b HAR tests). We introduce a class of nonstationary processes that have a time-varying spectral representation which evolves continuously except at a finite number of time points. We present an extension of the classical heteroskedasticity and autocorrelation consistent (HAC) estimators that applies two smoothing procedures. One is over the lagged autocovariances, akin to classical HAC estimators, and the other is over time. The latter element is important to flexibly account for nonstationarity. We name them double kernel HAC (DK-HAC) estimators. We show the consistency of the estimators and obtain an optimal DK-HAC estimator under the mean squared error (MSE) criterion. Overall, HAR tests standardized by the proposed DK-HAC estimators are competitive with fixed-b HAR tests, when the latter work well, with regards to size control even when there is strong dependence. Notably, in those empirically relevant situations in which previous HAR tests are undersized and have little or no power, the DK-HAC estimator leads to tests that have good size and power.

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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., Perron, P (2021) Prewhitened long-run variance estimation robust to nonstattionarity self1.000123100%
2Newey, W.K., West, K.D (1987) A simple positive semidefinite, heteroskedastic and autocorrelation consistent covariance matrix1.00083100%
3Casini, A., Deng, T., Perron, P (2021) Theory of low frequency contamination from nonstationarity and misspecification: consequences for HAR inference self1.00073100%
4Andrews, D.W.K (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation0.96721890%
5Kiefer, N.M., Vogelsang, T.J., Bunzel, H (2000) Simple robust testing of regression hypotheses0.87492100%
6Dahlhaus, R (1997) Fitting time series models to nonstationary processes0.8746467%
7Giacomini, R., Rossi, B (2009) Detecting and predicting forecast breakdowns0.87462100%
8Lazarus, E., Lewis, D.J., Stock, J.H (2020) The size-power tradeoff in HAR inference0.87462100%
9Priestley, M.B (1981) Spectral Analysis and Time Series0.8435360%
10Dahlhaus, R (2012) Locally stationary processes0.84333100%

Showing the top 10 of 90 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
1Change-Point Analysis of Time Series with Evolutionary Spectra0.96195
2Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference0.956167
3The Fixed-$b$ Limiting Distribution and the ERP of HAR Tests Under Nonstationarity0.941125
4Simultaneous Bandwidths Determination for DK-HAC Estimators and Long-Run Variance Estimation in Nonparametric Settings0.815377
5Prewhitened Long-Run Variance Estimation Robust to Nonstationarity0.807407
6Generalized Laplace Inference in Multiple Change-Points Models0.73732
7Backward CUSUM for Testing and Monitoring Structural Change with an Application to COVID-19 Pandemic Data0.51121
8Variance Estimation with Dependence and Heterogeneous Means0.51121
9Fast Online Changepoint Detection0.40511
10Dynamic Local Average Treatment Effects in Time Series0.40511