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 Y-1,..., Y-n. Following Zeger (Biometrika 75 (1988) 621-629), we suppose that the serial correlation depends on an unobservable latent process {epsilon(t)}. Assuming that the conditional distribution of Y-t given epsilon(t) belongs to the exponential family, that Y-l\epsilon(l),..., Y-n\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. (C) 2000 Elsevier Science B.V. All rights reserved.