Estimation of the linear quadratic model, the workhorse of the inventory literature, traditionally takes inventories and sales to be first-difference stationary series, and the ratio of the two variables to be stationary. However, these assumptions do not always match the properties of the data for the last two decades in the United States. We propose a model that allows for the non-stationary characteristics of the data, using polynomial cointegration. We show that the closed-form solution has other recent models as special cases. The resulting model performs well on aggregate and disaggregated data.