摘要翻译：
本文提出了一种新的跳扩散过程的阈值-核跳检测方法，该方法以近似最优的方式迭代应用阈值和核方法，以获得改进的有限样本性能。我们以期望的跳跃误分类数为目标函数，对跳跃检测方案的阈值参数进行优化选择。我们证明了目标函数是拟凸的，并得到了闭式最优阈值的一个新的二阶填充逼近。近似最优阈值不仅取决于现货波动率，还取决于起跑点的跳跃强度和跳跃密度值。然后开发了这些量的估计方法，其中现货波动率由带阈值的核估计器估计，在原点处的跳跃密度值由应用于被认为包含由选定阈值准则所确定的跳跃的增量的密度核估计器估计。由于模型参数与估计它们的近似最优估计量之间的相互依赖关系，提出了一种迭代不动点算法来实现模型参数。对典型随机波动率模型的仿真研究表明，高阶局部最优门限方案不仅可行，而且优于仅基于一阶近似和/或基于估计时间段内参数平均值的方案。
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英文标题：
《Optimal Iterative Threshold-Kernel Estimation of Jump Diffusion
  Processes》
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作者：
Jos\'e E. Figueroa-L\'opez, Cheng Li, and Jeffrey Nisen
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最新提交年份：
2020
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分类信息：

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
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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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
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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。
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英文摘要：
  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. 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.
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PDF链接：
https://arxiv.org/pdf/1811.07499