Skip Navigation


Biometrika Advance Access originally published online on July 1, 2009
Biometrika 2009 96(3):735-749; doi:10.1093/biomet/asp029
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
96/3/735    most recent
asp029v1
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Davis, R. A.
Right arrow Articles by Wu, R.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 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


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.