Bayesian Dynamic Tensor Regression

High- and multi-dimensional array data are becoming increasingly available. They admit a natural representation as tensors call for appropriate statistical tools. We propose new linear autoregressive tensor process (ART) tensor-valued data, that encompasses some well-known time series models special cases. study its properties derive the associated impulse response function. exploit PARAFAC low-rank decomposition providing parsimonious parameterization develop Bayesian inference allowing shrinking effects. apply ART model to of multilayer networks propagation shocks across nodes, layers time.