B1701
Title: Matrix autoregressive model with vector time series covariates for spatiotemporal data
Authors: Hu Sun - University of Michigan, Ann Arbor (United States) [presenting]
Zuofeng Shang - New Jersey Institute of Technology (United States)
Yang Chen - University of Michigan (United States)
Abstract: A new model is proposed for forecasting time series data distributed on a matrix-shaped spatial grid, using the historical spatio-temporal data together with auxiliary vector-valued time series data. The matrix time series are modelled as an auto-regressive process, where a future matrix is jointly predicted by the historical values of the matrix time series as well as an auxiliary vector time series. The matrix predictors are associated with row/column-specific autoregressive matrix coefficients that map the predictors to the future matrices via a bi-linear transformation. The vector predictors are mapped to matrices by taking a mode product with a 3D coefficient tensor. Given the high dimensionality of the tensor coefficient and the underlying spatial structure of the data, it is proposed to estimate the tensor coefficient by estimating one function coefficient for each covariate, with a 2D input domain, from a reproducing Kernel Hilbert space. The autoregressive matrix coefficients and the functional coefficients are jointly estimated under a penalized maximum likelihood estimation framework, and those are coupled with an alternating minimization algorithm. Large sample asymptotics of the estimators are established under fixed and high dimensionality and performances of the model are validated with extensive simulation studies and a real data application to forecast the global total electron content distributions.
