Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models
可能误设与非平稳模型中异方差和自相关稳健推断的演化谱理论AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要明确围绕非平稳经济时间序列的演化谱、长期方差和 HAC 推断展开，直接属于时间序列方向。
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可能误设与非平稳模型中异方差和自相关稳健推断的演化谱理论
- 研究问题
- 当经济时间序列因参数变化或模型误设而不满足二阶平稳性时，如何构造长期方差估计，改善稳健检验的尺寸与功效？
- 方法与思路
- 作者引入具有分段连续时变谱表示的过程，并在滞后自协方差与时间两个维度上平滑，形成双核 HAC 估计及其均方误差优化。
- 材料陈述的贡献
- 摘要称，论文证明双核 HAC 估计的一致性并给出均方误差意义下的最优估计，在若干既有方法表现欠佳的情形改善尺寸与功效。
- 阅读关注点
- 应核对过程类别、有限不连续点的处理、两个带宽及核函数的选择，并确认最优性和检验表现结论依赖哪些正则条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未经核验；摘要未给出完整条件、最优核形式或数值比较，不能认定对所有误设均稳健。
原文摘要
We develop a theory of evolutionary spectra for heteroskedasticity and autocorrelation robust (HAR) inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic time series which may arise either from parameter variation or model misspecification. In such a context, the theories that support HAR inference are either not applicable or do not provide accurate approximations. HAR tests standardized by existing long-run variance estimators then may display size distortions and little or no power. This issue can be more severe for methods that use long bandwidths (i.e., fixed-b HAR tests). We introduce a class of nonstationary processes that have a time-varying spectral representation which evolves continuously except at a finite number of time points. We present an extension of the classical heteroskedasticity and autocorrelation consistent (HAC) estimators that applies two smoothing procedures. One is over the lagged autocovariances, akin to classical HAC estimators, and the other is over time. The latter element is important to flexibly account for nonstationarity. We name them double kernel HAC (DK-HAC) estimators. We show the consistency of the estimators and obtain an optimal DK-HAC estimator under the mean squared error (MSE) criterion. Overall, HAR tests standardized by the proposed DK-HAC estimators are competitive with fixed-b HAR tests, when the latter work well, with regards to size control even when there is strong dependence. Notably, in those empirically relevant situations in which previous HAR tests are undersized and have little or no power, the DK-HAC estimator leads to tests that have good size and power.