Additive and innovational outliers in autoregressive time series: a unified bayesian approach

Abstract

A Bayesian approach is adopted to the analysis of autoregressive time series subject to outliers. Additive and innovational outliers are considered as particular cases of a mixed generating model, which allows one to handle situations in which there may be an unknown number of outliers of unknown type. In the paper an exact form of the likelihood function is used and stationarity of the model is enforced. The computational problems are solved using a version of the single component Metropolis-Hastings algorithm. The method proposed allows one to obtain all posterior summaries of interest including also the posterior probability that each observation is an outlier of additive and innovational type. An example with a real data set illustrates the usefulness of the methodology.