In recent years the theoretical restrictions of consumer demand have been examined in post sample forecasting exercises. However, this work has uniformly ignored the concavity restrictions of consumer demand. In this paper we evaluate a series of Normalized Quadratic Inverse Demand System (NQIDS) specifications using rolling windows and generating one-- to four--step ahead forecasts. To estimate the models, eleven categories of South Atlantic fish are used from 1980 through 2001. In addition to the NQIDS, we also examine the forecasting performance of a purely time series model. We find that the best predictions are achieved using a composite forecast.