The project will develop new statistical methods to analyze stochastic phenomena that inherently evolves in time. The methods will be based on high-frequency monitoring of the phenomena under study, which is of widening use in many fields such as finance, meteorology, biology, neuroscience, turbulence, statistical physics, seismology, and telecommunication. Thus, the research will foster more interaction between applied scientists and statisticians. The research and educational elements of the project will also serve as a training tool for both undergraduate and graduate students by forming synergistic research groups involving all levels.
Nonparametric methods are powerful statistical tools to reduce the model misspecification error, and high-frequency-based statistical analysis is a natural route to take when estimating the fine statistical features of continuous-time stochastic processes. Though the literature combining these two approaches has grown significantly during the last two decades, comparatively little work has been done to analyze and correct the sensitivity of methods to tuning parameters. The project will address these needs by (i) developing a unified approach for optimal kernel estimation of the spot volatility of an Ito process in the presence of leverage and microstructure noise; (ii) devising of optimal jump detection and integrated variance estimation methods, under the presence of stochastic volatility and infinite jump activity, via thresholding or shrinkage of the process' increments or wavelet coefficients; (iii) establishing theoretical guarantees for the data-driven plugging implementation methods resulting from the optimal schemes.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
