Nonparametric Methods for Jump Processes Under Microstructure Noise

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。研究了受背景噪声污染或受随机时钟影响的连续时间跳跃过程的非参数方法。例如，在金融市场，背景噪音是交易方式的副产品，而随机时钟可以模拟非同步交易效应或经济活动的累积衡量标准。拟议的研究开发了通过确定适当的采样频率、偏差校正工具和数据驱动的模型选择标准来量化和减轻滋扰成分的影响的方法。这项工作的重点是为过程的跳跃部分得出推论。提出了三个具体的研究方向：(1)控制跳跃动态的无限维参数的自适应非参数方法；(2)将资产价格的市场微观结构纳入模型和统计方法；(3)扩展到更通用的带有跳跃的模型，如时变的Levy或加性过程。近年来，越来越复杂的概率模型被发展起来，以寻求纳入所考虑现象的真实性质。对偏离假定模型对推动这一现象的基本参数的统计估计所产生的影响进行系统研究的努力要少得多。然而，如果没有适当的统计方法，即使是最复杂的范例也只能在工业和其他领域产生有限的实际影响。预计拟议的工作将针对上述关键的执行问题，大大推进数学金融理论。此外，鉴于金融行业采用包含“泡沫”和潜在崩盘的风险规避模型的持续趋势，预计本研究将促进学术界和工业界之间的合作机会。对一种商品潜在的突然价格变动进行经验评估，对于制定适当的风险管理和投资战略至关重要。其他外展目标包括扩展时空不连续过程，这在环境科学等领域的需求越来越大。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The investigator studies nonparametric methods for continuous-time jump processes that are contaminated by a background noise, or are affected by random clocks. In financial markets, for instance, the background noise is a byproduct of the way trading takes place, while a random clock could model non-synchronous trading effects or a cumulative measure of economic activity. The proposed research develops methodologies to quantify and mitigate the effects of the nuisance components by determining appropriate sampling frequencies, bias correction tools, and data-driven model selection criteria. The focus of the work is on drawing inferences for the jump component of the process. Three concrete research directions are put forward: (1) Adaptive nonparametric methods for the infinite-dimensional parameter controlling the jump dynamics, (2) Incorporation of the market microstructure of asset prices into the model and the statistical methodology, and (3) Extensions to more versatile models with jumps such as time-changed Levy or additive processes.In recent years increasingly complex probabilistic models have been developed in a quest to incorporate the real nature of the phenomenon under consideration. Considerably less effort has been devoted to a systematic study of the effects that departures from the presumed model have in the statistical estimation of the underlying parameters driving the phenomenon. However, without an appropriate statistical methodology, even the most sophisticated paradigm produces only limited practical impact in industry and across other fields. The proposed work is expected to significantly advance the theory of mathematical finance by targeting the aforementioned critical implementation issues. Furthermore, in light of the ongoing trend by the financial industry to adopt risk-adverse models that incorporate "bubles" and potential crashes, the present research is expected to foster opportunities of collaboration between academia and industry. An empirical assessment of the potential sudden price shifts of a commodity is critical to develop appropriate risk-management and investment strategies. Other outreach objectives include extensions to spatio-temporal discontinuous processes which are increasingly in demand in fields such as in environmental sciences.