arXiv 4 Mar 2021 · Econometrics · publishedJournal of Econometrics (2022) · 17 citations (OpenAlex)
arXiv:2103.02981 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by appendix_command · 40% of the source is main text. Read the extracted text to check this.
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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Casini, A., Perron, P (2021) Prewhitened long-run variance estimation robust to nonstattionarity self | 1.000 | 12 | 3 | 100% |
| 2 | Newey, W.K., West, K.D (1987) A simple positive semidefinite, heteroskedastic and autocorrelation consistent covariance matrix | 1.000 | 8 | 3 | 100% |
| 3 | Casini, A., Deng, T., Perron, P (2021) Theory of low frequency contamination from nonstationarity and misspecification: consequences for HAR inference self | 1.000 | 7 | 3 | 100% |
| 4 | Andrews, D.W.K (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation | 0.967 | 21 | 8 | 90% |
| 5 | Kiefer, N.M., Vogelsang, T.J., Bunzel, H (2000) Simple robust testing of regression hypotheses | 0.874 | 9 | 2 | 100% |
| 6 | Dahlhaus, R (1997) Fitting time series models to nonstationary processes | 0.874 | 6 | 4 | 67% |
| 7 | Giacomini, R., Rossi, B (2009) Detecting and predicting forecast breakdowns | 0.874 | 6 | 2 | 100% |
| 8 | Lazarus, E., Lewis, D.J., Stock, J.H (2020) The size-power tradeoff in HAR inference | 0.874 | 6 | 2 | 100% |
| 9 | Priestley, M.B (1981) Spectral Analysis and Time Series | 0.843 | 5 | 3 | 60% |
| 10 | Dahlhaus, R (2012) Locally stationary processes | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 90 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.