| 高频数据瞬时波动率核估计的窗宽选择及算法研究 |
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| 引用本文： | 王江涛,周勇. 高频数据瞬时波动率核估计的窗宽选择及算法研究[J]. 中国管理科学, 2018, 26(7): 1-8. DOI: 10.16381/j.cnki.issn1003-207x.2018.07.001 |
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| 作者姓名： | 王江涛 周勇 |
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| 作者单位： | 1. 上海财经大学统计与管理学院, 上海 200433;2. 华中师范大学经济与工商管理学院, 湖北 武汉 430079;3. 中国科学院数学与系统科学研究院, 北京 100190 |
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| 基金项目： | 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项目（2008DP173182）；国家数学与交叉科学中心项目（2008DP173182）；上海财经大学创新团队支持计划项目（IRTSHUFE13122402）；教育部人文社会科学研究青年资助项目（15YJC910007） |
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| 摘 要： | 在瞬时波动率的各种估计量中，非参数估计量因其能准确地度量瞬时波动率，一直是学者们的研究热点。然而，这类估计量在实际应用中都面临着最优窗宽的确定问题。由于最优窗宽中往往携带一些难以估计的未知参数，使得在实际应用过程中确定最优窗宽的具体数值存在困难。本文以瞬时波动率的核估计量为例，借鉴非参数回归分析中窗宽选择的思想，构建了一种能从数据中准确计算出最优窗宽具体值的算法。理论的分析和数值上的验证表明：文中所构建的算法具有良好的稳定性、适应性和收敛速度。算法的提出为瞬时波动率的后续应用研究铺平道路。
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| 关 键 词： | 瞬时波动率 窗宽选择 核估计 |
| 收稿时间： | 2017-05-03 |
| 修稿时间： | 2017-07-10 |
Bandwidth Selection for Kernel Estimator of Spot Volatility in High Frequency data and Algorithm Design |
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| WANG Jiang-tao,ZHOU Yong. Bandwidth Selection for Kernel Estimator of Spot Volatility in High Frequency data and Algorithm Design[J]. Chinese Journal of Management Science, 2018, 26(7): 1-8. DOI: 10.16381/j.cnki.issn1003-207x.2018.07.001 |
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| Authors: | WANG Jiang-tao ZHOU Yong |
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| Affiliation: | 1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China;2. School of Economics and Business Administration, Huazhong Normal University, Wuhan 430079, China;3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | The non-parametric estimator of spot volatility is the current focus due to its high accuracy. However, this estimator has to choose the optimal bandwidth in its application. There is difficulty in calculating the optimal bandwidth since some awkward unknown parameters emerge. In this paper, taking kernel estimator as the representative of non-parametric estimator for spot volatility, a data-driven algorithm of bandwidth selection has been constructed by adopting some idea of non-parametric regression. The stability of algorithm for selecting bandwidth is proved in the theory. It is shown that the algorithm is adaptive and convergent with a fast rate from the numerical examples and the convergence is independent on the original value. The proposed algorithm is conductive to the subsequent analysis of spot volatility. |
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| Keywords: | spot volatility bandwidth selection kernel estimator |
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