Many demand time series experience temporary shocks, such as through calendar effects or sales campaigns. In a network with geographically dispersed locations, shocks may seem to be regionally contained. However, their effects can be global which then have to be accounted for when forecasting demand. We propose a linear multivariate state space model to model the global effects of regional temporary shocks through a latent process. We further propose two regularization strategies to address the large set of coefficients that are required to model complex demand time series. Our first proposal is a penalized likelihood method with a grouped penalization of the model coefficients. In addition, we consider the model coefficient regularization through Bayesian priors. We compare the empirical forecasting performance of our model against benchmark models on a demand dataset of a large container shipping company.