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We consider the derivation of data-dependent simultaneous bandwidths fordouble kernel heteroskedasticity and autocorrelation consistent (DK-HAC)estimators. In addition to the usual smoothing over lagged autocovariances forclassical HAC estimators, the DK-HAC estimator also applies smoothing over thetime direction. We obtain the optimal bandwidths that jointly minimize theglobal asymptotic MSE criterion and discuss the trade-off between bias andvariance with respect to smoothing over lagged autocovariances and over time.Unlike the MSE results of Andrews (1991), we establish how nonstationarityaffects the bias-variance trade-o?. We use the plug-in approach to constructdata-dependent bandwidths for the DK-HAC estimators and compare them with theDK-HAC estimators from Casini (2021) that use data-dependent bandwidthsobtained from a sequential MSE criterion. The former performs better in termsof size control, especially with stationary and close to stationary data.Finally, we consider long-run variance estimation under the assumption that theseries is a function of a nonparametric estimator rather than of asemiparametric estimator that enjoys the usual T^(1/2) rate of convergence.Thus, we also establish the validity of consistent long-run variance estimationin nonparametric parameter estimation settings.

Simultaneous Bandwidths Determination for DK-HAC Estimators and Long-Run Variance Estimation in Nonparametric Settings