BINOMIAL AUTOREGRESSIVE PROCESSES WITH DENSITY‐DEPENDENT THINNING

Abstract

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 overdispersion and underdispersion, as well as positive and negative autocorrelations. We derive a law of large numbers and a central limit theorem, which provide useful large‐ N approximations for various quantities of interest.