Statistical inference for the doubly stochastic self-exciting process
Statistical inference for the doubly stochastic self-exciting process
复制标题
双随机自激过程的统计推断
DOI：
10.3150/17-bej966
复制
发表时间：
2016
期刊：
影响因子：
1.5
通讯作者：
Yoann Potiron
中科院分区：
文献类型：
--
作者：
Simon Clinet;Yoann Potiron
我们引入并证明了核呈指数递减且参数时变的Hawkes自激点过程的存在性。兴趣量定义为积分参数$T^{-1}\int_0^T\theta_t^*dt$，其中$\theta_t^*$为时变参数，并考虑高频渐近。为了估计它naïvely，我们将数据分成几个块，计算每个块上的最大似然估计器（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non-naïve估计量，该估计量被构造为对局部MLE应用一阶偏差约简时的naïve估计量。我们给出了相关的中心极限定理。蒙特卡罗模拟表明了偏差校正的重要性，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。
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.
高频数据中的局部参数估计
影响因子：
3
作者：
Potiron, Yoann;Mykland, Per
通讯作者：
Mykland, Per
影响因子：
6.3
作者：
Potiron, Yoann;Mykland, Per A.
通讯作者：
Mykland, Per A.