关于金融高频数据的统计推断

In today's world, many fields are confronted with increasingly large amounts of data. Financial data sampled with high frequency is no exception. These staggering amounts of data pose special challenges to the world of finance, as traditional models and information technology tools can be poorly suited to grapple with their size and complexity. Probabilitstic modeling and statistical data analysis attempt to discover order from apparent disorder. It is well known that the high frequency data have some unique characteristics that do not appear in lower frequencies, such as jumps, microstructure noise non-synchronous trading. Thus, analysis of these data introduces many new challenges to financial economists and statisticians since the classical theory on stochastic processes and statistics is no longer enough to solve the mentioned problems. The purpose of this project is to investigate some of the issues in the study of high frequency financial data by proposing some appropriate statistical models and methods. These are interesting and challenging problems in statistical modeling and also very useful in finance. We will study these special characteristics, consider methods for analyzing high frequency data, and discuss the potential application of the results obtained. In particular, we propose method for model selection problem under the simultaneous presence of jumps and microstructure noise effect, investigate the jumps, microstructure noise and non-synchronous effects on the co-volatility estimation. The models and methodologies discussed in this project are also applicable to other scientic areas such as telecommunications and environmental studies.

随着社会经济的急速发展，关于金融高频数据中涉及到的各项指标的研究已引起了人们广泛的关注，尤其对股票、期货及其衍生物在组合管理、风险分析等方面的分析更是受到人们的高度重视。本项目拟在我们近几年研究的基础上，进一步从伊藤过程与分数布朗运动的特性出发，结合高频数据对资产价格的潜在过程进行研究。其研究意义在于，理论上，我们通过对资产价格中关注的一些指标进行估计，同时对资产价格的驱动过程进行一系列的检验，可以进一步丰富高频数据、金融统计与极限理论等方面的理论知识；应用上，所得的结果在资产价格、电信与环境的真实数据分析中也有指导性的作用。

随着科学技术与电子产品的急速发展，利用秒、毫秒甚至纳米秒所采集到的数据，越来越受到人们的重视，围绕该数据，即高频数据或超高频数据，来探讨它们在经济、金融、保险、概率与统计等方面的应用，正是当前研究的重要课题之一。. 利用一系列非参数估计的方法，本项目分别解决了高频数据在带noise的伊藤过程或带noise的半鞅模型时，关于一维的自权重积分波动率的估计问题；二维时的积分波动率的估计问题；低维的时间具有内生性时的波动率的估计问题，以及在高维时带有稀疏条件下的关于积分波动率矩阵的估计等一系列问题。在理论上，我们的研究成果促进了高频数据在金融、经济、统计与极限理论等方面的发展；在应用上，我们的研究成果对资产价格在组合管理、风险分析等方面也有指导性的作用。目前已发表或待发表论文6篇，参加了4次国际会议，6次学术交流。