Recently, the paper “On the Modeling and Prediction of High-Dimensional Functional Time Series”, jointly completed by Professor Jinyuan Chang, Assistant professor Qin Fang at the University of Sydney, Associate professor Xinghao Qiao at the University of HongKong and Professor Qiwei Yao from the London School of Economics and Political Science has been officially accepted by Journal of the American Statistical Association.
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, executive director of the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics, Guanghua distinguished professor, and recipient of the National Science Fund for Distinguished Young Scholars of China. Mainly engaged in two research fields: ultra-high dimensional data analysis and high-frequency financial data analysis.
Qin Fang, assistant professor at the University of Sydney, primarily conducts research in the fields of dynamic network analysis, functional data/time series analysis, and high-dimensional statistics.
Xinghao Qiao, associate professor at the University of HongKong. Mainly engaged in research in the fields of functional data analysis, complex time series analysis, high-dimensional statistics, and non parametric Bayesian analysis.
Qiwei Yao , chair professor at the London School of Economics and Political Science, UK, fellow of Institute of Mathematical Statistics，elected member of International Statistical Institute, fellow of American Statistical Association. Mainly engaged in research in the fields of time series analysis, high-dimensional time series modeling and prediction, dimensionality reduction and factor modeling, dynamic network modeling, spatiotemporal modeling, financial econometrics, and non parametric regression.
