Bayesian outlier detection in INGARCH time series
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Date
2012-07-12
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Abstract
INGARCH models for time series of counts arising, e.g., in
epidemiology assume the observations to be Poisson distributed conditionally
on the past, with the conditional mean being an affinelinear
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. Such outliers are difficult
to handle 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 if
there are some outliers in the data.
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Keywords
Additive Outliers, Generalized Linear Models, Level Shift, Time Series of Counts