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Bayesian Analysis of Order Uncertainty in ARIMA Models

In this paper we extend the work of Brooks and Ehlers (2002) and Brooks et al. (2003) by constructing efficient proposal schemes for reversible jump MCMC in the context of autoregressive moving average models. In particular, the full conditional distribution is not available for the added parameters and approximations to it are provided by suggesting an adaptive updating scheme which automatically selects proposal parameter values to improve the efficiency of between-model moves. The performance of the proposed algorithms is assessed by simulation studies and the methodology is illustrated by applying it to a real data set.