Collaborative Research: Statistical Inference for Multivariate and Functional Time Series via Sample Splitting

Multivariate and functional time series are prevalent and routinely collected in many fields. Statistical inference of such time series is a fundamental problem in modern time series analysis and has broad applications in many scientific areas, including bioinformatics, business, climate science, economics, finance, genetics, and signal processing. Compared with existing methodologies, this research project will provide nonparametric inference procedures that can accommodate a wide range of dimensionality and require weak assumptions on the data generating processes. The methodology ensuing from the project will be disseminated to the relevant scientific communities via publications, conference and seminar presentations, and the development of open-source software. The project will involve multiple research mentoring initiatives, including efforts on broadening participation, and will offer advanced topic courses to introduce the state-of-the-art techniques in time series analysis. The project will provide a broad range of interdisciplinary training opportunities at all educational levels and will contribute to the future workforce professional development. The project will develop a systematic body of methods and theory on inference for both multivariate (including high-dimensional) time series and functional time series based on sample splitting (SS) and self-normalization (SN). Recently, the SN technique has been advanced to the inference of high-dimensional time series, but it requires the use of a trimming parameter. Also, its scope of applicability is limited to high-dimensional time series with weak panel dependence which might be unrealistic in many modern time series applications. In turn, the existing SN for functional time series relies on dimension reduction by functional principal component analysis and, hence, the resulting procedure may be powerless when the alternative is orthogonal to the space spanned by the top principal components used in the procedure. To address these major limitations, this project will develop a new unified framework based on SS-SN, in conjunction with inference for multivariate and functional time series, and investigate its utility in application to analysis of time series of low, medium, high or infinite dimensions. 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.