We present a novel specification of a dynamic multinomial ordered choice model, where the latent variable is a function of strictly stationary exogenous variables and lags of the choice variable. We prove that such a model with weakly dependent errors will have a strictly stationary solution which is L-2 near epoch dependent. We also derive consistency and asymptotic normality of the maximum likelihood estimator for a probit specification of the model. We illustrate a possible application of the model by estimating a discrete version of a robust ``difference" monetary policy rule for the period 1990:2006 at a monthly frequency.