Herein, we focus on an end-to-end design of a proactive cooperative caching strategy for a multi-cell network. The design is challenging as it involves two interrelated problems: the ability to predict future content popularity and to meet network operation characteristics. To this end, we first formulate a cooperative content caching in order to optimize the aggregated network cost for delivering contents to users. An efficient proactive caching policy requires an accurate prediction of time-varying content popularity. Content popularity has temporal and spatial dependencies and therefore, we develop a probabilistic dynamical model for content popularity prediction by exploiting its spatiotemporal correlations. To achieve an accurate tracking and prediction of content popularity evolution, the proposed dynamical model is non-linear and incorporates non-Gaussian distributions. We use Variational Bayes (VB) approach for estimating the model parameters. The VB provides mathematical tractability. We then develop an online VB method that works with streaming data where content request arrives sequentially. Using extensive simulations study on a real-world dataset, we show that our online VB based dynamical model provides improved performance compared to conventional content caching policies.