英文标题：
《Optimum thresholding using mean and conditional mean square error》
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作者：
Jos\\\'e E. Figueroa-L\\\'opez and Cecilia Mancini
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最新提交年份：
2017
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英文摘要：
  We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is constructed using observations on a discrete time grid, and precisely it sums up the squared increments of the process when they are below a threshold, a deterministic function of the observation step and possibly of the coefficients of X. All the threshold functions satisfying given conditions allow asymptotically consistent estimates of IV, however the finite sample properties of the truncated realized variation can depend on the specific choice of the threshold. We aim here at optimally selecting the threshold by minimizing either the estimation mean square error (MSE) or the conditional mean square error (cMSE). The last criterion allows to reach a threshold which is optimal not in mean but for the specific volatility (and jumps paths) at hand. A parsimonious characterization of the optimum is established, which turns out to be asymptotically proportional to the L\\\'evy\'s modulus of continuity of the underlying Brownian motion. Moreover, minimizing the cMSE enables us to propose a novel implementation scheme for approximating the optimal threshold. Monte Carlo simulations illustrate the superior performance of the proposed method.
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中文摘要：
我们考虑一个资产价格（对数）的一元半鞅模型，其中包含可能具有无限活动（IA）的跳跃。Mancini 2009年提出的综合方差IV的非参数阈值估值器是使用离散时间网格上的观测值构建的，当其低于阈值时，它精确地求出了过程的平方增量，观测步长的确定函数，可能是X的系数的确定函数。所有满足给定条件的阈值函数都允许对IV进行渐近一致的估计，但是截断实现变量的有限样本特性可能取决于阈值的具体选择。我们的目标是通过最小化估计均方误差（MSE）或条件均方误差（cMSE）来优化选择阈值。最后一个标准允许达到一个阈值，该阈值不是平均值，而是针对手头的特定波动率（和跳跃路径）的最优阈值。建立了最优解的一个简约特征，它与基础布朗运动的L’evy连续模成渐近比例。此外，最小化cMSE使我们能够提出一种新的实现方案来逼近最佳阈值。蒙特卡罗仿真表明了该方法的优越性能。
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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
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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