A nonparametric estimation procedure for the Hawkes process: comparison with maximum likelihood estimation
A nonparametric estimation procedure for the Hawkes process: comparison with maximum likelihood estimation
复制标题
霍克斯过程的非参数估计过程：与最大似然估计的比较
DOI：
10.1080/00949655.2017.1422126
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发表时间：
2018
影响因子：
1.2
通讯作者：
A. Bercher
中科院分区：
文献类型：
--
作者：
Matthias Kirchner;A. Bercher
在早期的工作中，Kirchner [霍克斯过程的估计程序。量化金融2017;17（4）：571-595]，我们介绍了Hawkes点过程的非参数估计方法。在本文中，我们提出了一个模拟研究，比较这种特定的非参数方法的最大似然估计。我们发现，这两种估计方法的标准差下降的幂律的样本容量。此外，标准偏差是成比例的。例如，对于一个特定的霍克斯模型，分支系数估计值的标准偏差比MLE大约大20%-在所有考虑的样本量内。当真实的基础分支系数变大时，该因子变小。在运行时间方面，我们的方法明显优于MLE。我们的方法目前的偏见可以很好地解释和控制。作为一个偶然的发现，我们看到，也MLE估计似乎是显着偏置时，潜在的霍克斯模型是接近临界。这就要求对霍克斯似然及其优化进行更严格的分析。
ABSTRACT In earlier work, Kirchner [An estimation procedure for the Hawkes process. Quant Financ. 2017;17(4):571–595], we introduced a nonparametric estimation method for the Hawkes point process. In this paper, we present a simulation study that compares this specific nonparametric method to maximum-likelihood estimation. We find that the standard deviations of both estimation methods decrease as power-laws in the sample size. Moreover, the standard deviations are proportional. For example, for a specific Hawkes model, the standard deviation of the branching coefficient estimate is roughly 20% larger than for MLE – over all sample sizes considered. This factor becomes smaller when the true underlying branching coefficient becomes larger. In terms of runtime, our method clearly outperforms MLE. The present bias of our method can be well explained and controlled. As an incidental finding, we see that also MLE estimates seem to be significantly biased when the underlying Hawkes model is near criticality. This asks for a more rigorous analysis of the Hawkes likelihood and its optimization.