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英文文献：Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach-高采样频率下的局部分布推断:Bootstrap方法
英文文献作者：Ulrich Hounyo,Rasmus T. Varneskov
英文文献摘要：
We study inference for the local innovations of It^o semimartingales. Specifically, we construct a resampling procedure for the empirical CDF of high-frequency innovations that have been standardized using a nonparametric estimate of its stochastic scale (volatility) and truncated to rid the effect of "large" jumps. Our locally dependent wild bootstrap (LDWB) accommodate issues related to the stochastic scale and jumps as well as account for a special block-wise dependence structure induced by sampling errors. We show that the LDWB replicates first and second-order limit theory from the usual empirical process and the stochastic scale estimate, respectively, as well as an asymptotic bias. Moreover, we design the LDWB sufficiently general to establish asymptotic equivalence between it and and a nonparametric local block bootstrap, also introduced here, up to second-order distribution theory. Finally, we introduce LDWB-aided Kolmogorov-Smirnov tests for local Gaussianity as well as local von-Mises statistics, with and without bootstrap inference, and establish their asymptotic validity using the second-order distribution theory. The finite sample performance of CLT and LDWB-aided local Gaussianity tests are assessed in a simulation study as well as two empirical applications. Whereas the CLT test is oversized, even in large samples, the size of the LDWB tests are accurate, even in small samples. The empirical analysis verifies this pattern, in addition to providing new insights about the distributional properties of equity indices, commodities, exchange rates and popular macro finance variables.
我们研究了半鞅局部创新的推理。具体地说，我们为高频创新的经验CDF构建了一个重采样程序，使用其随机尺度(波动率)的非参数估计进行标准化，并进行截断以消除“大”跳变的影响。我们的局部依赖野自举(LDWB)适应与随机尺度和跳跃相关的问题，并解释了一个特殊的块依赖结构的抽样误差。我们证明了LDWB分别从通常的经验过程和随机尺度估计复制了一阶和二阶极限理论，以及一个渐近偏差。此外，我们设计了足够普遍的LDWB，以建立它与非参数局部块自举之间的渐近等价，这里也介绍了，直到二阶分布理论。最后，我们介绍了在自举推理和不自举推理的情况下，利用ldw辅助的Kolmogorov-Smirnov检验局部高斯性和局部冯-米赛斯统计量，并利用二阶分布理论建立了它们的渐近有效性。在一个模拟研究和两个经验应用中，评估了CLT和ldwb辅助的局部高斯性测试的有限样本性能。尽管CLT测试是超大的，即使在大样本中，LDWB测试的大小是准确的，即使在小样本中。实证分析验证了这一模式，并对股票指数、商品、汇率和流行的宏观金融变量的分布特性提供了新的见解。
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