Self- and cross-excitation in point processes are commonly captured in the financial econometrics literature using a multivariate exponential memory kernel. In this article, the exponential assumption is relaxed and the resultant non-parametric memory kernel is estimated by a method based on second-order cumulants. The estimator is shown to be consistent and asymptotically normally distributed and performs well under simulation. An empirical application based on 10 international stock indices is presented. Two different indices of contagion between markets are constructed from the point process models in order to examine interconnection over time. A conclusion which emerges from these results is the assumption that a parametric kernel may be too restrictive as the application reveals interesting features, and in some cases substantial differences, between the exponential and non-parametric kernels.

中文翻译：

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估计互激发点过程的非参数内存内核

点过程中的自激和交叉激励通常在金融计量经济学文献中使用多元指数内存内核来捕获。本文放宽了指数假设，采用基于二阶累积量的方法估计得到的非参数内存核。估计量显示为一致且渐近正态分布，并且在模拟下表现良好。提出了一个基于 10 个国际股票指数的实证应用。从点过程模型中构建了两个不同的市场之间传染指数，以便检查一段时间内的相互联系。从这些结果中得出的一个结论是假设参数内核可能过于严格，因为应用程序揭示了有趣的特征，并且在某些情况下存在实质性差异，