On autocorrelation in a Poisson regression model

This paper develops a practical approach to diagnosing the existence of a l atent stochastic process in the mean of a Poisson regression model. The asy mptotic distribution of standard generalised linear model estimators is der ived for the case where an autocorrelated latent process is present. Simple formulae for the effect of autocovariance on standard errors of the regres sion coefficients are also provided. Methods for adjusting for the severe b ias in previously proposed estimators of autocovariance are derived and the ir behaviour is investigated. Applications of the methods to time series of monthly polio counts in the U.S.A. and daily asthma presentations at a hos pital in Sydney are used to illustrate the results and methods.