Limit theorems for regression models of time series of counts

Here we present some limit theorems for a general class of generalized linear models describing time series of counts Y1,...,Yn. Following Zeger (Biometrika 75 (1988) 621-629), we suppose that the serial correlation depends on an unobservable latent process {[var epsilon]t}. Assuming that the conditional distribution of Yt given [var epsilon]t belongs to the exponential family, that Y1[var epsilon]1,...,Yn[var epsilon]n are independent, and that the latent process satisfies a mixing condition, it is shown that the quasi-likelihood estimators of the regression coefficients are asymptotically normally distributed.