Inference for Multi‐dimensional High‐frequency Data with an Application to Conditional Independence Testing
Inference for Multi‐dimensional High‐frequency Data with an Application to Conditional Independence Testing
复制标题
多维高频数据推理及其在条件独立性测试中的应用
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
P. Mykland
中科院分区：
文献类型：
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作者：
M. Bibinger;P. Mykland
我们发现了具有微观结构的高频金融数据的多维多尺度和核估计的渐近分布。采样时间允许是异步的和内源性的。在这个过程中，我们证明了平滑噪声扰动的多尺度估计和核估计类在相应的核函数和权函数具有相同的渐近分布的意义上是渐近等价的。该理论导出了多维稳定中心极限定理和可行的版本。因此，它们允许为广泛的多变量模型进行统计推断，这为由高频率观察资产组成的任意投资组合的风险度量中的测试和置信区间铺平了道路。作为一个应用程序，我们加强了方法来构建一个测试的假设，相关的资产是独立的条件下的一个共同的因素。
We find the asymptotic distribution of the multi‐dimensional multi‐scale and kernel estimators for high‐frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that the classes of multi‐scale and kernel estimators for smoothing noise perturbation are asymptotically equivalent in the sense of having the same asymptotic distribution for corresponding kernel and weight functions. The theory leads to multi‐dimensional stable central limit theorems and feasible versions. Hence, they allow to draw statistical inference for a broad class of multivariate models, which paves the way to tests and confidence intervals in risk measurement for arbitrary portfolios composed of high‐frequently observed assets. As an application, we enhance the approach to construct a test for investigating hypotheses that correlated assets are independent conditional on a common factor.