A Re-interpretation of the Linear-Quadratic Model When Inventories and Sales are Polynomially Cointegrated

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 to be stationary. However, these assumptions do not match the properties of the data for the last two decades in the US and the UK. We offer 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 and shows good forecasting properties.