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