摘要翻译：
我们定义了一种数值方法，给出了对称多元Hawkes过程核形状的非参数估计。该方法依赖于Hawkes过程的二阶统计特性，它将过程的协方差矩阵与核矩阵联系起来。利用最小相位恢复方法计算相关函数的平方根。我们用一些例子说明了我们的方法，并提供了估计误差的实证研究。在此框架内，我们分析了一维或二维Hawkes过程模型下的高频金融价格数据。我们发现缓慢衰减的（幂律）核形状表明价格动力学微观结构水平上的自激现象具有长记忆性质。
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英文标题：
《Non-parametric kernel estimation for symmetric Hawkes processes.
  Application to high frequency financial data》
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作者：
E. Bacry, K. Dayri and J. F. Muzy
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最新提交年份：
2011
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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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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英文摘要：
  We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation function is computed using a minimal phase recovering method. We illustrate our method on some examples and provide an empirical study of the estimation errors. Within this framework, we analyze high frequency financial price data modeled as 1D or 2D Hawkes processes. We find slowly decaying (power-law) kernel shapes suggesting a long memory nature of self-excitation phenomena at the microstructure level of price dynamics.
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PDF链接：
https://arxiv.org/pdf/1112.1838