COMPOSITE LIKELIHOOD FOR TIME SERIES MODELS WITH A LATENT AUTOREGRESSIVE PROCESS

Consistency and asymptotic normality properties are proved for various composite likelihood estimators in a time series model with a latent Gaussian autoregressive process. The proofs require different techniques than for clustered data with the number of clusters going to infinity. The composite likelihood estimation method is applied to a count time series consisting of daily car accidents with weather related covariates. A simulation study for the count time series model shows that the performance of composite likelihood estimator is better than Zeger's moment-based estimator, and the relative efficiency is high with respect to approximate maximum likelihood.