Case Studies Modeling Count Conditional Distributions

• Activity Number: 310
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Robert Jung*+ and A.R. Tremayne
• Companies: Univesitaet Hohenheim and University of New South Wales and University of Liverpool
• Keywords: Integer autoregression ; regression effects ; PIT histogram ; scoring rules ; generalized Poisson distribution

Abstract

This paper is concerned with using different modelling approaches to specification, estimation and diagnostic checking for time series models of (low) counts. The methods used are especially well-suited to modelling stock-type data, rather than count incidence data. Rarely, if ever, is there just a single approach to modelling that might be adopted. Here we consider in detail the use of two classes of models and their associated conditional distributions: integer autoregressive models (with regression effects); and those from the autoregressive conditional mean family. Both are used in conjunction with three novel data sets that differ according to dispersion, serial correlation and conditional mean variation due to exogenous components. Parameter estimation is generally done by maximum likelihood methods and a rigorous attempt is made to examine the adequacy of fitted models. A range of different models transpire to be preferred across the set of applications. We conclude that model specification search in this field needs to entertain different types of models for good subsequent application of forecasting or prediction which we consider to be a principal aim of modelling.