2021/02/26 by Federico Belotti, Belotti, Federico, Alessandro Casini +7 · 1 citation
Mathematics · #Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2103.00060
openalex publication_date 2021/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the derivation of data-dependent simultaneous bandwidths for\ndouble kernel heteroskedasticity and autocorrelation consistent (DK-HAC)\nestimators. In addition to the usual smoothing over lagged autocovariances for\nclassical HAC estimators, the DK-HAC estimator also applies smoothing over the\ntime direction. We obtain the optimal bandwidths that jointly minimize the\nglobal asymptotic MSE criterion and discuss the trade-off between bias and\nvariance with respect to smoothing over lagged autocovariances and over time.\nUnlike the MSE results of Andrews (1991), we establish how nonstationarity\naffects the bias-variance trade-o?. We use the plug-in approach to construct\ndata-dependent bandwidths for the DK-HAC estimators and compare them with the\nDK-HAC estimators from Casini (2021) that use data-dependent bandwidths\nobtained from a sequential MSE criterion. The former performs better in terms\nof size control, especially with stationary and close to stationary data.\nFinally, we consider long-run variance estimation under the assumption that the\nseries is a function of a nonparametric estimator rather than of a\nsemiparametric estimator that enjoys the usual T^(1/2) rate of convergence.\nThus, we also establish the validity of consistent long-run variance estimation\nin nonparametric parameter estimation settings.\n