Optimal iterative threshold-kernel estimation of jump diffusion processes
Optimal iterative threshold-kernel estimation of jump diffusion processes
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DOI：
10.1007/s11203-020-09211-7
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发表时间：
2020-03
影响因子：
0.8
通讯作者：
José E. Figueroa-López;Cheng Li;Jeffrey A. Nisen
中科院分区：
文献类型：
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作者：
José E. Figueroa-López;Cheng Li;Jeffrey A. Nisen
在本文中，我们提出了一种新的跳跃扩散过程的阈值-核跳跃检测方法，该方法以近似最优的方式迭代地应用阈值和核方法来获得改进的有限样本性能。与Figueroa-López和Nisen （Stoch Process Appl 123(7): 2648-2677, 2013）一样，我们使用期望的跳错分类数作为目标函数，以最优选择跳检测方案的阈值参数。我们证明了目标函数是拟凸的，并得到了最优阈值的一个新的二阶填充近似的封闭形式。近似最优阈值不仅与点波动率有关，还与跳跃强度和原点处的跳跃密度值有关。然后开发了这些量的估计方法，其中现场波动率由带有阈值的核估计器估计，原点处的跳跃密度值由密度核估计器估计，该密度核估计器应用于根据所选阈值标准认为包含跳跃的增量。由于模型参数与为估计模型参数而建立的近似最优估计量之间存在相互依赖性，因此提出了一种迭代不动点算法来实现模型参数。对一个典型随机波动模型的仿真研究表明，高阶局部最优阈值方案不仅可行，而且优于仅基于一阶近似和/或参数在估计时段内的平均值的方案。
In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. As in Figueroa-López and Nisen (Stoch Process Appl 123(7):2648–2677, 2013), we use the expected number of jump misclassifications as the objective function to optimally select the threshold parameter of the jump detection scheme. We prove that the objective function is quasi-convex and obtain a new second-order infill approximation of the optimal threshold in closed form. The approximate optimal threshold depends not only on the spot volatility, but also the jump intensity and the value of the jump density at the origin. Estimation methods for these quantities are then developed, where the spot volatility is estimated by a kernel estimator with thresholding and the value of the jump density at the origin is estimated by a density kernel estimator applied to those increments deemed to contain jumps by the chosen thresholding criterion. Due to the interdependency between the model parameters and the approximate optimal estimators built to estimate them, a type of iterative fixed-point algorithm is developed to implement them. Simulation studies for a prototypical stochastic volatility model show that it is not only feasible to implement the higher-order local optimal threshold scheme but also that this is superior to those based only on the first order approximation and/or on average values of the parameters over the estimation time period.