Modelling Matrix Time Series via a Tensor CP-Decomposition

Speaker：Prof. Qiwei Yao (The London School of Economics and Political Science)

Date：March 3 Fri. 3:00 pm

Venue：Tencent Meeting Room: 921-141-544

Abstract：We consider modelling matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation. This refined method significantly improves the finite-sample performance of the estimation. The asymptotic theory has been established under a general setting without the stationarity. It shows, for example, that all the component coefficient vectors in the CP-decomposition are estimated consistently with certain convergence rates. The proposed model and the estimation method are also illustrated with both simulated and real data, showing effective dimension-reduction in modelling and forecasting matrix time series.

(Joint work with Jinyuan Chang, Jing He and Lin Yang)