DK-HAC: Double Kernel Heteroskedasticity and Autocorrelation Consistent Estimator and Robust Standard Errors

Keywords: HAC, DK-HAC, Robust Standard Errors, HAR, Long-run variance, Prewhitening, Covariance Matrix.

This software implements the DK-HAC covariance matrix estimators and robust standard errors from Casini (2021) and Casini and Perron (2021b).

The DK-HAC estimator extends the Newey-West's (1987, 1994) and Andrews' (1991) HAC estimators to flexibly account for nonstationarity (e.g., breaks, time-varying parameters/volatility, regime swicthing, misspecification, outliers, etc.). See Casini et al. (2021) for a technical comparison.

The software includes ordinary functions for regression analysis with robust (DK-HAC) standard errors including t-test, F-test, standard errors, R-squared and other popular regression outputs.

The software also includes the following tools:

• Data-dependent methods for the choice of the number of lagged autocovariances as developed in Belotti et al. (2021) and Casini (2021).
• Prewhitening procedure as developed in Casini and Perron (2021b).
• Pre-test for nonstationarity to improve the finite-sample performance as developed in Casini and Perron (2021a).

Non-Technical Summary for Empirical Research

In preparation.

Software available in Matlab, R and Stata

• Matlab Package (to be uploaded later)
• R Package (to be uploaded later)
• Stata Package (to be uploaded later)

Contributors

• Federico Belotti, University of Rome Tor Vergata.
• Alessandro Casini, University of Rome Tor Vergata.
• Leopoldo Catania, Aarhus University.
• Taosong Deng, Boston University.
• Stefano Grassi, University of Rome Tor Vergata.
• Pierre Perron, Boston University.

Background Papers

• Belotti, F., A. Casini, L. Catania, S. Grassi and P. Perron, "Simultaneous Bandwidths Determination for DK-HAC Estimators and Long-Run Variance Estimation in Nonparametric Settings". arXiv preprint arXiv.
• Casini, A. (2019), "Improved Methods for Statistical Inference in the Context of Various Types of Parameter Variation". Ph.D Dissertation, Boston University.
• Casini, A. (2021), "Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models". arXiv preprint arXiv.
• Casini, A. and P. Perron (2021a), "Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference". arXiv preprint arXiv
• Casini, A. and P. Perron (2021a), "Change-Point Analysis of Time Series with Evolutionary Spectra". arXiv preprint arXiv
• Casini, A. and P. Perron (2021b), "Minimax MSE Bounds and Nonlinear VAR Prewhitening for Long-Run Variance Estimation Under Nonstationarity". arXiv preprint arXiv

Maintainer and Correspondence

• Alessandro Casini, University of Rome Tor Vergata.