摘要翻译：
本文考虑了两个资产价格由一个无漂移的具有无限活动性的跳跃的半区间生成，并在高频上有规律地同步观察时，采用协整概念的一个框架。我们发展了一种基于回归的协整关系估计方法，并在该框架内证明了当存在协整时相关的相合性和中心极限理论。我们还提供了一个基于Dickey-Fuller型残差的无协整零检验和它的极限理论。在无协整条件下，其渐近极限与原Dickey-Fuller残差检验的渐近极限相同，因此临界值可以用同样的方法计算出来。有限样本表明在各种实际配置中具有足够的尺寸和良好的功率特性，优于原始的Dickey-Fuller和Phillips-Perron型基于残差的测试，这些基于残差的测试的尺寸因非遍历时变方差而失真，功率因价格跳变而改变。两个经验例子巩固了蒙特卡罗证据，即适应的测试可以被拒绝，而原始的测试不能，反之亦然。
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英文标题：
《Cointegration in high frequency data》
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作者：
Simon Clinet and Yoann Potiron
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最新提交年份：
2021
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless It\^{o}-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high frequency. We develop a regression based estimation of the cointegrated relations method and show the related consistency and central limit theory when there is cointegration within that framework. We also provide a Dickey-Fuller type residual based test for the null of no cointegration against the alternative of cointegration, along with its limit theory. Under no cointegration, the asymptotic limit is the same as that of the original Dickey-Fuller residual based test, so that critical values can be easily tabulated in the same way. Finite sample indicates adequate size and good power properties in a variety of realistic configurations, outperforming original Dickey-Fuller and Phillips-Perron type residual based tests, whose sizes are distorted by non ergodic time-varying variance and power is altered by price jumps. Two empirical examples consolidate the Monte-Carlo evidence that the adapted tests can be rejected while the original tests are not, and vice versa.
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PDF链接：
https://arxiv.org/pdf/1905.07081