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）资助的。研究者研究了被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，在金融市场中，背景噪声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度量。拟议的研究开发的方法来量化和减轻滋扰组件的影响，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。这项工作的重点是对过程的跳跃部分进行推断。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，和（3）扩展到更通用的模型与跳跃，如时间-近年来，为了结合所考虑的现象的真实的性质，已经开发了越来越复杂的概率模型。系统研究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的努力要少得多。 然而，如果没有适当的统计方法，即使是最先进的范例也只能在工业和其他领域产生有限的实际影响。预计拟议的工作将通过针对上述关键实施问题显着推进数学金融理论。 此外，鉴于金融业目前的趋势是采用包含“泡沫”和潜在崩溃的风险不利模型，预计目前的研究将促进学术界和产业界之间的合作机会。对商品价格可能突然变动的经验性评估对于制定适当的风险管理和投资战略至关重要。其他推广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.