英文标题：
《Statistical inference for the doubly stochastic self-exciting process》
---
作者：
Simon Clinet and Yoann Potiron
---
最新提交年份：
2017
---
英文摘要：
We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter $T^{-1}\\int_0^T\\theta_t^*dt$, where $\\theta_t^*$ is the time-varying parameter, and we consider the high-frequency asymptotics. To estimate it na\\\"ively, we chop the data into several blocks, compute the maximum likelihood estimator (MLE) on each block, and take the average of the local estimates. The asymptotic bias explodes asymptotically, thus we provide a non-na\\\"ive estimator which is constructed as the na\\\"ive one when applying a first-order bias reduction to the local MLE. We show the associated central limit theorem. Monte Carlo simulations show the importance of the bias correction and that the method performs well in finite sample, whereas the empirical study discusses the implementation in practice and documents the stochastic behavior of the parameters.
---
中文摘要：
我们引入并证明了具有指数递减核且参数是时变的Hawkes自激点过程的存在性。感兴趣的数量定义为积分参数$T ^{-1}\\int\\u 0^T\\theta\\u T ^*dt$，其中$\\ theta\\u T ^*$是时变参数，我们考虑高频渐近。为了简单地估计它，我们将数据分成几个块，计算每个块上的最大似然估计量（MLE），并取局部估计的平均值。渐近偏差渐近爆炸，因此我们提供了一个非简单估计量，它被构造为na\\“当对局部极大似然估计应用一阶偏差缩减时，我们给出了相关的中心极限定理。蒙特卡罗模拟显示了偏差修正的重要性，并且该方法在有限样本中表现良好，而实证研究讨论了在实践中的实现，并记录了参数的随机行为。
---
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
--
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

---
PDF下载：
-->