The paper “On the Modeling and Prediction of High-Dimensional Functional Time Series”, co-authored by Prof. Jinyuan Chang, Assistant Prof. Qin Fang from the University of Sydney, Prof. Xinghao Qiao from the University of Hong Kong, and Prof. Qiwei Yao from the London School of Economics and Political Science, has been officially accepted by the Journal of the American Statistical Association, one of the top journals in the field of statistics.
Abstract
We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series p is large in relation to the length of time series n. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from any two different groups are uncorrelated both contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the transformed functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modeling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulation and two real datasets. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
Author Introduction
Jinyuan Chang is the Executive Director of the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics. He is a Guanghua Distinguished Professor and a recipient of the National Science Fund for Distinguished Young Scholars of China. His research primarily focuses on ultra-high dimensional data analysis and high-frequency financial data analysis.
Qin Fang is an Assistant Professor at the University of Sydney. Her research interests include dynamic network analysis, functional data and time series analysis, and high-dimensional statistics.
Xinghao Qiao is an Associate Professor at the University of Hong Kong. His research focuses on functional data analysis, complex time series analysis, high-dimensional statistics, and nonparametric Bayesian analysis.
Qiwei Yao is a Chair Professor at the London School of Economics and Political Science. He is a Fellow of the Institute of Mathematical Statistics, an Elected Member of the International Statistical Institute, and a Fellow of the American Statistical Association. His research areas include time series analysis, high-dimensional time series modeling and prediction, dimensionality reduction and factor modeling, dynamic network modeling, spatiotemporal modeling, financial econometrics, and nonparametric regression.
