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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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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中文摘要：
本文针对跳跃扩散过程提出了一种新的阈值核跳跃检测方法，该方法以近似最优的方式迭代应用阈值和核方法，以提高有限样本性能。我们以期望的跳跃错误分类数为目标函数，优化选择跳跃检测方案的阈值参数。我们证明了目标函数是拟凸的，并以闭形式得到了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，还取决于跳变强度和原点跳变密度的值。然后开发这些量的估计方法，其中现货波动率由带阈值的核估计器估计，原点跳跃密度的值由密度核估计器估计，密度核估计器应用于所选阈值准则认为包含跳跃的增量。由于模型参数与为估计它们而建立的近似最优估计量之间的相互依赖性，开发了一种迭代不动点算法来实现它们。对一个典型随机波动率模型的仿真研究表明，实施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/或估计时间段内参数平均值的方案。
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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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