Content caching at base stations is an effective solution to cope with the unprecedented data traffic growth by prefetching contents near to end-users. To proactively servicing users, it is of high importance to extract predictive information from data requests. In this paper, we propose an accurate content request prediction algorithm for improving the performance of edge caching systems. In particular, we develop a Bayesian dynamical model through which a complex nonlinear latent temporal trend structure in the content requests can be accurately tracked and predicted. The dynamical model also leverages tensor train decomposition to capture content-location interactions to further enhance the accuracy of predictions. To infer the model's parameters, we derive an approximation of the posterior distribution based on variational Bayes (VB) method with an embedded Kalman smoother algorithm. Based on the predictions of the proposed model, we design a cost-efficient proactive cooperative caching policy which adaptively utilizes network resources and optimizes the content delivery. The advantage of the proposed caching scheme is demonstrated via numerical results using two real-world datasets, which show that the developed Bayesian dynamical model substantially outperforms reference methods that ignore the temporal trends and content-location interactions.