Dynamic Factor Model for Poisson Time Series in Matrix and Tensor Form

In many applications, we often encounter integer-valued time series observations in the form of tensors (multi-dimensional array). Motivated by the applications in geo-political event prediction, crime data analysis and transportation and trading networks modeling, in this paper we study the modeling, interpretation and prediction for Poisson tensor time series through dynamic factor models. The approach contains an observation layer specified for the Poisson distribution, and a latent layer to account for the dynamic and concurrent dependence. The dynamics is introduced through the factor structure with tensor Tucker decomposition. We propose an autocovariance-based approach to estimate the loading matrices and vectors, which takes advantage of the dependence to reduce the noise level. The estimation of the factors is through an efficient computational method for Poisson Lon-Normal regression model. An autoregressive modeling of the factors is considered to enable the predictions. Theoretical investigations and numerical experiments are presented.

Host: Xiaofeng Shao