英文标题：
《Testing the causality of Hawkes processes with time reversal》
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作者：
Marcus Cordi, Damien Challet, Ioane Muni Toke
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最新提交年份：
2017
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英文摘要：
We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.
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中文摘要：
我们证明了单变量和对称多变量Hawkes过程仅具有弱因果关系：真实事件时间向量和反向事件时间向量的真实对数似然几乎相等，因此通过最大似然进行参数估计仅弱依赖于时间箭头的方向。在理想（合成）条件下，参数拟合优度测试明确拒绝向后的事件时间，这意味着从时间对称量（如事件率的自方差）推断核，很少产生具有统计意义的拟合。最后，我们发现，对于同一事件时间向量，使用多个参数核拟合金融数据可能会对两个时间箭头产生显著的拟合，有时有利于向后的时间方向。这表明，霍克斯过程对具有灵活内核的真实数据的显著拟合并不意味着一个明确的时间箭头，除非对其进行测试。
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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：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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