The information era has witnessed an explosion in the collection of high dimensional time series data across a wide range of areas, including finance, signal processing, neuroscience, meteorology, seismology, among others. For low dimensional time series, there is a well-developed estimation and inference theory. Inference theory in the high dimensional setting is of fundamental importance and has wide applications, but has been rarely studied. Researchers face a number of challenges in solving real-world problems: (i) complex dynamics of data generating systems, (ii) temporal and cross-sectional dependencies, (iii) high dimensionality and (iv) non-Gaussian distributions. The goal of this project is to develop and advance inference theory for high dimensional time series data by concerning all the above characteristics. The project will provide training to graduate students and publicly avaialble statistical packages.

This project involves developing a systematic asymptotic theory for estimation and inference for high dimensional time series, including parameter estimation, construction of simultaneous confidence intervals, prediction, model selection, Granger causality test, hypothesis testing, and spectral domain estimation. To this end, a new methodology for the estimation of parameters and second-order characteristics for high dimensional time series will be proposed. New tools and concentration inequalities for the asymptotic analysis of high-dimensional time series will be developed. To perform simultaneous inference and significance testing, the PIs will investigate the very deep Gaussian approximation problem and the high dimensional central limit theorems by taking both high dimensionality and temporal and cross-sectional dependencies into account.

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.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1916290
Program Officer
Huixia Wang
Project Start
Project End
Budget Start
2019-08-01
Budget End
2022-07-31
Support Year
Fiscal Year
2019
Total Cost
$120,000
Indirect Cost
Name
University of California San Diego
Department
Type
DUNS #
City
La Jolla
State
CA
Country
United States
Zip Code
92093