科学研究

Xinghao Qiao obtained his PhD in Business Statistics from Marshall School of Business at the University of Southern California. He is currently a tenured associate professor of Statistics at the London School of Economics and Political Science. His research areas include functional data analysis, time series analysis, high-dimensional statistical inference, Bayesian nonparametrics and etc. Many of his research papers have been published in top Statistics and Econometrics journals such as Journal of the American Statistical Association, Biometrika, Journal of Econometrics and Journal of Business and Economic Statistics. 

We propose a two-step procedure to model and predict high-dimensional functional time series, where the number p of function-valued variables is large in relation to the number n of serially dependent observations. Our first segmentation step uses the eigenanalysis of a positive definite matrix to look for linear transformation of original high-dimensional functional time series such that the transformed curve series can be segmented into multiple groups of low-dimensional subseries, and the subseries in different groups are uncorrelated both contemporaneously and serially. Modelling each low-dimensional subseries separately will not lose the overall linear dynamical information, and at the same time, can avoid the overparametrization issue arisen from directly modelling original high-dimensional curve series. Our second dimension-reduction step estimates the finite-dimensional dynamical structure for each group of the transformed curve series that converts the problem of modelling low-dimensional functional time series to that of modelling vector time series. Efficient strategies can be implemented to predict vector time series groupwisely, which can then be converted back to predict groups of transformed curve subseries and finally original functional time series. We investigate the theoretical properties of our proposal when p diverges at an exponential rate of n. The superior finite-sample performance of the proposed methods is illustrated through both extensive simulations and three real datasets.