Due to the rapid development of information technologies and their applications in many scientific fields, high dimensional time series (HDTS) are routinely collected nowadays. The methods and theory developed for the inference of low and fixed dimensional time series may not be applicable when the dimension is comparable to or exceeds time series length, and there is an urgent need to develop new statistical methods that can accommodate both high dimensionality and temporal dependence. Statistical inference for HDTS is fundamentally important and has many applications in disciplines ranging from climate science to medical imaging and finance, among others.
This project aims to develop innovative theory and methodologies to address several important inference problems in the analysis of HDTS. The research is built on the self-normalized approach, which has found great success in dealing with low dimensional problems. Its advance to the high dimensional context is challenging both methodologically and theoretically, and it requires a new methodological formulation and new theory. This project covers the inference of the mean, covariance matrix, and auto-covariance matrix for HDTS, and the tests developed can be used to detect change points, certain structure of the covariance matrix and target dense alternative. On the theoretical front, the weak convergence of sequential U-statistic based process will be investigated and is of independent interest.
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.
