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Statistica Sinica 21 (2011), 279-305





COMPOSITE LIKELIHOOD FOR TIME SERIES MODELS

WITH A LATENT AUTOREGRESSIVE PROCESS


Chi Tim Ng, Harry Joe, Dimitris Karlis and Juxin Liu


Hong Kong Polytechnic University, University of British Columbia,
Athens University of Economics and Business, and University of Saskatchewan


Abstract: 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.



Key words and phrases: Asymptotic normality, consistency, count data, Gauss-Hermite quadrature, pairwise likelihood, random effects.

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