Habit persistence in time series models of discrete choice

We provide a framework for modelling habit persistence in choice that integrates vector auto-regressive and moving-average (VARMA) time-series models with random coefficient Multinomial Probit (MNP) models. We provide two classes of models. In the first we assume that the error in the utility function has a general VARMA structure, and in the second we assume that structure for the regression coefficients. We provide an interpretation of these two classes of models. As an illustration, we re-analyse the A.C. Nielsen Company 1986/1987 scanner panel data on ketchup purchases and compare our model with two alternative state dependence models.