Nonparametric Methods for Jump Processes Under Microstructure Noise

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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.