On autocorrelation in a Poisson regression model

This paper develops a practical approach to diagnosing the existence of a latent stochastic process in the mean of a Poisson regression model. The asymptotic distribution of standard generalised linear model estimators is derived for the case where an autocorrelated latent process is present. Simple formulae for the effect of autocovariance on standard errors of the regression coefficients are also provided. Methods for adjusting for the severe bias in previously proposed estimators of autocovariance are derived and their behaviour is investigated. Applications of the methods to time series of monthly polio counts in the USA and daily asthma presentations at a hospital in Sydney are used to illustrate the results and methods.