報告時間： 2019年12月12日周四下午15:00~16:30

報告地點： X2511

報告題目: High-dimensional vector autoregressive time series modeling via tensor decomposition

Abstract:

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to rearrange the coefficient matrices of the model into a tensor form such that the parameter space can be restricted in three directions simultaneously via tensor decomposition. The proposed method substantially expands the capacity of vector autoregressive modeling for a large number of time series. In contrast, the widely used reduced-rank regression method can restrict the parameter space in only one direction. Moreover, to handle high-dimensional time series, this paper considers imposing sparsity on factor matrices to improve the interpretability and estimation efficiency, which leads to a sparsity-inducing estimator. For the low-dimensional case, we derive asymptotic properties of the proposed least squares estimator and introduce an alternating least squares algorithm. For the high-dimensional case, we establish non-asymptotic properties of the sparsity-inducing estimator and propose an ADMM-based algorithm for regularized estimation. Simulation experiments and a real data example demonstrate the advantages of the proposed approach over various existing methods.

報告人簡介：李國棟，2007年于香港大學統(tǒng)計精算系獲得統(tǒng)計學博士，隨后在南洋理工大學任助理教授?，F(xiàn)任香港大學統(tǒng)計精算系副教授。主要研究方向包括時間序列分析，分位數(shù)回歸，高維統(tǒng)計數(shù)據(jù)分析和機器學習。李教授目前發(fā)表學術論文40余篇，其中若干篇發(fā)表在統(tǒng)計學4大頂級期刊，以及計量經濟學的頂級期刊Journal of Econometrics上。