Recently, the paper “An autocovariance based learning framework for high-dimensional functional time series” jointly completed by Professor Jinyuan Chang and postdoctoral researcher Cheng Chen from the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics, Associate Professor Xinghao Qiao from the London School of Economics, and Professor Qiwei Yao has been officially accepted by the top international academic journal of econometrics.
Abstract
This paper investigates how to estimate high-dimensional functional time series models of interest based on observations with noise pollution, and proposes a “three-step” framework: firstly, an operator is constructed based on the autocorrelation information of the observation sequence, and the estimation problem of functional parameters in the original model is transformed into a parameter estimation problem in Euclidean space through spectral decomposition of the operator; Then, block regularized minimum distance estimation about unknown parameters in Euclidean space is obtained through autocovariance information; Finally, the obtained estimate will be transformed into an estimate of the functional parameters in the original model through a one-to-one mapping. This article systematically studies the theoretical properties of the proposed method and analyzes the convergence speed of corresponding estimates on three high-dimensional functional time series models: “scalar function regression”, “function function regression”, and “function vector autoregression”. Numerical simulation and case analysis demonstrate the superiority of the proposed method.
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, Doctoral Supervisor, recipient of the National Science Fund for Distinguished Young Scholars of China, Sichuan Province Distinguished Expert, and member of the Sichuan Province Statistical Expert Advisory Committee. Mainly engaged in research in two fields: ultra-high dimensional data analysis and high-frequency financial data analysis.
Cheng Chen, a postdoctoral fellow at the School of Statistics, Southwestern University of Finance and Economics, with Professor Chang Jinyuan as his co supervisor. Mainly engaged in research in the fields of functional data analysis and high-dimensional time series analysis.
Xinghao Qiao, Associate Professor at the London School of Economics and Political Science, UK, 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.
