Generalized Autoregressive Dirichlet Multinomial Models: Definition and Stability

Abstract

The need for a dynamic framework in discrete time for multicategory choice processes is examined. A state-space model to describe the evolution of a Dirichlet-Multinomial multicategory choice system with strong temporal correlation is developed, forecasting formulæ are derived and the conditions for long term stability in the mean are developed. A first order undifferenced process (AR = 1,MA = 1) is constructed for the controlling parameters of a Dirichlet-Multinomial distribution from which choice counts are drawn. This process is suitable to model the results of public opinion and consumer surveys where there is an expectation that preferences will drift over time without violating the distributional assumptions of the counting process itself. The constructed process thus possesses a structure analogous to the General Linear Model when used to model binary decisions but is extended to a richer distributional family.

Keywords: time-series analysis, survey analysis, GARCH, Dirichlet-Multinomial

JEL Classification: C02, C32