Generalized choice models for categorical time series

The NDARMA models of Jacobs and Lewis (1983) allow the modeling of categorical processes with an ARMA-like serial dependence structure. These models can be represented through a backshift mechanism, and we analyze marginal and bivariate properties of the resulting backshift process. Motivated by this backshift mechanism, we define the new class of generalized choice (GC) models, which include the usual NDARMA models as a special case, and we derive results describing the marginal and bivariate distribution of the GC model. We discuss implications concerning DMA(∞) models and the serial dependence structure of NDARMA models. Examples show that the family of GC models allows creating sparsely parametrized models for categorical processes with different types of serial dependence structure.