Estimation for unequally spaced time series of counts with serially correlated random effects

Abstract

A generalized model for time series count data with serially correlated random effects is introduced to establish robust inference procedures. Observations are taken at possibly unequally spaced time intervals and random effects are assumed to have a stationary ergodic continuous time first-order autoregressive process. This is a generalization of Zeger (Biometrika 75 (1988) 621) where observations are taken at equally spaced time intervals and random effects are assumed to follow a discrete autoregressive process. For reasons of robustness, the distributional forms of random effects is not specified. The central limit theorem is established to prove asymptotic normality of estimators.