The proposal aims to advance statistical theory for random processes that exhibit features like long-range dependence and nonlinearities, and to educate both statisticians and others scientists in this new exciting area. Compared to the well-developed theory under the independence assumption, it is considerably more challenging to establish a limit theory for processes with such features. The Principal Investigator proposes a powerful martingale based method and studies spectral estimation, empirical processes, nonparametric estimation and other related asymptotic problems for such processes.
Processes with long-range dependence and nonlinearities occur in various fields, including computer networks, communication, finance, geology, hydrology, econometrics and atmospheric science among others. Applications of the research results developed in the proposal would help test and justify claims made by scientists in such fields. In particular, the PI develops statistical methodology to identify trends in temperature and ozone sequences and provides statistical reasoning for meteorologists' claims on climate change patterns.
