A simple dynamic model for limited dependent variables

A dynamic model for limited dependent variables is proposed, which estimation does not rely on simulation methods. A latent conditional mean function which is measurable with respect to past and observable information circumvents the solution of a T-dimensional integral and yields a simple and computationally parsimonious maximum likelihood estimation. It can be shown that the latent process implied by the limited dependent autoregressive moving average model is covariance stationary. Parameter estimates of this model are shown to be consistent but inefficient estimates of the parameters of a standard latent autoregressive moving average model, for which a maximum likelihood estimator is computationally burdensome. Monte Carlo evidence is provided to asess parameter estimates based on the limited dependent ARMA given the data generation process is a standard latent ARMA. The results indicate that the asymptotic properties hold quite nicely in small samples. An application based on IBM transaction price changes from the NASDAQ demonstrates a potential use of the model suggested here.