We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite-sample properties under nonstationarity (i.e., fixed-b methods), or are theoretically valid under the null hypothesis but lead to tests that are not consistent under nonstationary alternative hypothesis (i.e., both fixed-b and traditional HAC estimators). The proposed estimator accounts explicitly for nonstationarity, unlike previous prewhitened procedures which are known to be unreliable, and leads to tests with accurate null rejection rates and good monotonic power. We also establish MSE bounds for LRV estimation that are sharper than previously established and use them to determine the data-dependent bandwidths.

翻译：我们引入了非参数非线性VAR预白长期差异(LRV)估算器,用于构建在包括线性回归模型在内的各种情况下可用于假设测试的标准差,以构建对自动调节和电传偏振度具有强力的标准差,在包括线性回归模型在内的各种情况下可用于假设测试。现有的方法在理论上是有效的,在不连续状态下(即固定方法),其有限的抽样特性较低,或者在理论上根据无效假设是有效的,但导致在非静止假设下(即固定b和传统的 HAC估计器)进行不一致的测试。提议的估算器与先前的预白程序不同,不可靠,明确记录了非静止性,并导致以准确的无效拒绝率和良好的单声波功率进行测试。我们还为LRCV估算设定了比以前确立的精确度强的 MSE界限,并使用这些界限来确定数据依赖的带宽度。