The hierarchy of correlations is an approximation scheme which permits the study of non-equilibrium phenomena in strongly interacting quantum many-body systems on lattices in higher dimensions (with the underlying idea being somewhat similar to dynamical mean-field theory). So far, this method was restricted to equal-time correlators such as ⟨ A ˆ μ ( t ) B ˆ ν ( t ) ⟩ . Using the method of complete induction, we generalize this method to double-time correlators such as ⟨ A ˆ μ ( t ) B ˆ ν ( t ′ ) ⟩ . The hierarchical decoupling scheme permits the evaluation of correlation functions in thermal equilibrium as well as in non-equilibrium settings. As an application, we study the equilibrium dynamics of correlation functions and the related light-cone structure of the bosonic Hubbard model in the Mott insulator phase. Furthermore we address the light-cone structure when the system is quenched.