Most studies of inventory consolidation effects assume time-independent random demand. In this article, we consider time-dependence by incorporating an autoregressive moving average structure to model the demand for products. With this modeling approach, we analyze the effect of consolidation on inventory costs compared to a system without consolidation. We formulate an inventory setting based on continuous-review using allocation rules for regular transshipment and centralization, which establishes temporal structures of demand. Numerical simulations demonstrate that, under time-dependence, the demand conditional variance, based on past data, is less than the marginal variance. This finding favors dedicated locations for inventory replenishment. Additionally, temporal structures reduce the costs of maintaining safety stocks through regular transshipments when such temporal patterns exist. The obtained results are illustrated with an example using real-world data. Our investigation provides information for managing supply chains in the presence of time-patterned demands that can be of interest to decision-makers in the supply chain.