Autoregressive Negative Binomial Processes

Web - based Supplementary Materials for “ Chain Binomial Models and Binomial Autoregressive Processes ”

Binomial Autoregressive Processes with Density Dependent Thinning

We present an elaboration of the usual binomial AR(1) process on {0, 1, . . . , N} that allows the thinning probabilities to depend on the current state n only through the “density” n/N , a natural assumption in many real contexts. We derive some basic properties of the model and explore approaches to parameter estimation. Some special cases are considered that allow for overand underdispersion...

Chain binomial models and binomial autoregressive processes.

We establish a connection between a class of chain-binomial models of use in ecology and epidemiology and binomial autoregressive (AR) processes. New results are obtained for the latter, including expressions for the lag-conditional distribution and related quantities. We focus on two types of chain-binomial model, extinction-colonization and colonization-extinction models, and present two appr...

Parameter Estimates for Fractional Autoregressive Spatial Processes

A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular , it is shown thatˆdN − d = OP ((Log N) 3 N), where d = (d1, d2) denotes the long memory parameter.

Bivariate binomial autoregressive models

This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued...