Retrospective Bayesian outlier detection in INGARCH series

INGARCH models for time series of counts arising, e.g., in epidemiology or finance assume the observations to be Poisson distributed conditionally on the past, with the conditional mean being an affine-linear function of the previous observations and the previous conditional means. We model outliers within such processes, assuming that we observe a contaminated process with additive Poisson distributed contamination, affecting each observation with a small probability. Our particular concern are additive outliers, which do not enter the dynamics of the process and can represent measurement artifacts and other singular events influencing a single observation. Retrospective analysis of such outliers is difficult within a non-Bayesian framework since the uncontaminated values entering the dynamics of the process at contaminated time points are unobserved. We propose a Bayesian approach to outlier modeling in INGARCH processes, approximating the posterior distribution of the model parameters by application of a componentwise Metropolis-Hastings algorithm. Analyzing real and simulated data sets, we find Bayesian outlier detection with non-informative priors to work well in practice when there are some outliers in the data.