Many companies invest in various marketing efforts, such as price promotion and advertising, in order to attract new customers and build customer loyalty. This paper examines the problem of setting efficient inventory levels when new marketing efforts are made and product demand is autocorrelated. We assume that the inventory manager operates with a base stock policy based on a critical fractile. If marketing has a temporary effect, the underlying demand tends to revert to a long-term equilibrium trend and the inventory manager needs to use a stationary demand model (e.g., autoregressive model) to determine the required inventory level. In contrast, if the effect is permanent, demand shocks contain an element that represents a permanent departure from previous levels and a non-stationary demand model (e.g., random walk) needs to be used instead. We show that the required inventory behaves much differently for the case of using a stationary demand model as opposed to a non-stationary model, but it is difficult in practice to identify a correct demand model in the absence of a long sampling span. In this paper, we propose an inventory model that explicitly acknowledges uncertainty over stationary and non-stationary demand models in response to new marketing efforts. The proposed model averages the inventory policies of the two demand models, weighted by each model's posterior probability. This is an extension of Bayesian model averaging. Simulation results demonstrate that the Bayesian model averaging inventory model improves the inventory system.