A formal derivation of a macroscopic model for unsteady and inertial one-phase incompressible flow in rigid and periodic porous media is presented using an upscaling technique. The resulting model is non-local in time and involves two effective coefficients in the macroscopic filtration law, namely a dynamic apparent permeability tensor and a vector accounting for the time-decaying influence of the flow initial condition. This model generalizes previous non-local macroscale models restricted to creeping flow conditions. Ancillary closure problems are provided, which allow computing the effective coefficients. Symmetry and positiveness analyses of the apparent permeability are carried out, evidencing that this tensor is symmetric only in the creeping regime. The effective coefficients are functions of time, geometry, macroscopic forcings and the initial flow condition. Predictions of the effective coefficients are made on a simple periodic structure for a wide range of Reynolds numbers smaller than the critical value characterizing the first Hopf bifurcation. Finally, the performance of the macroscopic model for a variety of macroscopic forcing and initial conditions is examined in four case studies along with validation with direct numerical simulations. It is shown that the purely heuristic classical model, widely used for unsteady flow, consisting in a Darcy-like model complemented with an accumulation term on the filtration velocity, is inappropriate.