非平稳性和模型不恰当性引起的低频污染理论：对HAR推断的影响
Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference
AI总结：
本文研究非平稳性和模型不恰当性导致的低频污染对HAR推断的影响，推导了样本自协方差和周期图的渐近偏倚表达式，并探讨了非参数平滑在低频污染下的稳健性。
摘要：
我们建立了关于由一般非平稳性引起的低频污染（即长期记忆效应）对估计量如样本自协方差和周期图的理论结果，并推导了对异方差和自相关稳健（HAR）推断的影响。我们给出了这些估计量的渐近偏倚的显式表达式。我们区分了低频污染仅在小样本问题中出现和在渐近中持续存在的两种情况。我们理论证明非参数时间平滑对低频污染具有稳健性。我们的结果提供了关于一致性和不一致长期方差（LRV）估计的争论的新见解。现有LRV估计器在数据非平稳时倾向于膨胀，导致HAR检验可能低估并表现出剧烈的统计功效损失。我们的理论表明，长带宽或固定-b HAR检验比基于HAC估计器的HAR检验更受低频污染影响，而最近引入的双核HAC估计器不受此问题影响。最后，我们给出了非平稳性下HAC和DK-HAC估计量及相应t检验在线性回归模型中的二阶Edgeworth展开。
英文摘要：
We establish theoretical results about the low frequency contamination (i.e., long memory effects) induced by general nonstationarity for estimates such as the sample autocovariance and the periodogram, and deduce consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We present explicit expressions for the asymptotic bias of these estimates. We distinguish cases where this contamination only occurs as a small-sample problem and cases where the contamination continues to hold asymptotically. We show theoretically that nonparametric smoothing over time is robust to low frequency contamination. Our results provide new insights on the debate between consistent versus inconsistent long-run variance (LRV) estimation. Existing LRV estimators tend to be in inflated when the data are nonstationary. This results in HAR tests that can be undersized and exhibit dramatic power losses. Our theory indicates that long bandwidths or fixed-b HAR tests suffer more from low frequency contamination relative to HAR tests based on HAC estimators, whereas recently introduced double kernel HAC estimators do not super from this problem. Finally, we present second-order Edgeworth expansions under nonstationarity about the distribution of HAC and DK-HAC estimators and about the corresponding t-test in the linear regression model.
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