INGARCH models for time series of counts arising, e.g., inepidemiology assume the observations to be Poisson distributed conditionallyon the past, with the conditional mean being an affinelinearfunction of the previous observations and the previous conditionalmeans. We model outliers within such processes, assuming thatwe observe a contaminated process with additive Poisson distributedcontamination, affecting each observation with a small probability. Ourparticular concern are additive outliers, which do not enter the dynamicsof the process and can represent measurement artifacts and othersingular events influencing a single observation. Such outliers are difficultto handle within a non-Bayesian framework since the uncontaminatedvalues entering the dynamics of the process at contaminated timepoints are unobserved. We propose a Bayesian approach to outlier modelingin INGARCH processes, approximating the posterior distributionof the model parameters by application of a componentwise Metropolis-Hastings algorithm. Analyzing real and simulated data sets, we findBayesian outlier detection with non-informative priors to work well ifthere are some outliers in the data.
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