基于高频数据采用非参数的方法估量波动率，因其能更准确地度量波动率，一直是学者们研究的热点.然而，波动率的所有非参数估计都面临着窗宽的选择问题.由于最优窗宽中往往携带一些难以估计的未知参数，使得在应用过程中确定最优窗宽的具体数值存在困难，从而阻碍了这类估计量的使用.本文以已实现核估计作为波动率非参数估计的代表，构建了一种能自动从实际数据中确定最优窗宽的算法.理论分析的结果表明：算法具有稳定性，其所确定的窗宽是最优窗宽的无偏一致估计量，收敛速度为O（n-1/5）.实际数据检验的结果显示，算法是稳定的并且具有良好的适应性，由算法确定的窗宽不依赖初始值的选取.模拟数据的结果显示，相比传统确定窗宽的方法，算法确定的窗宽所对应的估计量具有更高的精度.文中的算法可推广到波动率其他的非参数估计量中，从而为这类估计量的使用铺平道路.
Abstract
The non-parametric estimator of volatility based on high frequency data is the current focus due to its high accuracy. All of these estimator have to choose their optimal bandwidth in the application. However, it is difficult to calculate the optimal bandwidth from the real data and to apply these estimator, since optimal bandwidth always take some awkward unknown parameters. In this paper, taking realized kernel as the representative, a new data-driven algorithm for selecting the bandwidth has been constructed. The stability of algorithm is proved and the selected bandwidth is consistent estimator of optimal bandwidth without bias. The convergence rate is O(n-1/5). It is shown from the numerical examples that the algorithm is adaptive and the finally selected bandwidth is independent on the original value. Simulation result shows that the estimator for volatility with bandwidth selected by our algorithm has higher accuracy. The proposed algorithm could be modified to select optimal bandwidth for other non-parametric estimator of volatility as well.
关键词
波动率 /
已实现核估计 /
窗宽选择 /
算法设计
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Key words
volatility /
realize kernel /
bandwidth selection /
algorithm design
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中图分类号：
F830
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参考文献
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基金
国家自然科学基金委重点项目（71331006，91546202）；中国科学院重点实验室（2008DP173182）；上海财经大学创新团队支持计划（IRTSHUFE13122402）；教育部人文社会科学研究青年项目（15YJC910007）
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