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Biometrika Advance Access published online on July 1, 2009
Biometrika, doi:10.1093/biomet/asp029
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© 2009 Biometrika Trust

Article

A negative binomial model for time series of counts

Richard A. Davis

Department of Statistics, Columbia University, New York, New York 10027, U.S.A. rdavis{at}stat.columbia.edu

Rongning Wu

Department of Statistics and Computer Information Systems, Baruch College, The City University of New York, New York, New York 10010, U.S.A. rongning.wu{at}baruch.cuny.edu

Received for publication 1 February 2008. Revision received 1 December 2008.
  Abstract

We study generalized linear models for time series of counts, where serial dependence is introduced through a dependent latent process in the link function. Conditional on the covariates and the latent process, the observation is modelled by a negative binomial distribution. To estimate the regression coefficients, we maximize the pseudolikelihood that is based on a generalized linear model with the latent process suppressed. We show the consistency and asymptotic normality of the generalized linear model estimator when the latent process is a stationary strongly mixing process. We extend the asymptotic results to generalized linear models for time series, where the observation variable, conditional on covariates and a latent process, is assumed to have a distribution from a one-parameter exponential family. Thus, we unify in a common framework the results for Poisson log-linear regression models of Davis et al. (2000), negative binomial logit regression models and other similarly specified generalized linear models.

Key Words: Generalized linear model • Latent process • Negative binomial distribution • Time series of counts


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