In this thesis, a Bayesian approach is adopted to handle parameter estimation and model uncertainty in autoregressive moving average (ARMA) time series models and dynamic linear models (DLM). Bayesian model uncertainty is handled in a parametric fashion through the use of posterior model probabilities computed via Markov chain Monte Carlo (MCMC) simulation techniques. Attention is focused on reversible jump Markov chain Monte Carlo (RJMCMC) samplers, which can move between models of different dimensions, to address the problem of model order uncertainty and strategies for proposing efficient sampling schemes in autoregressive moving average time series models and dynamic linear models are developed. The general problem of assessing convergence of the sampler in a dimension-changing context is addressed by computing estimates of the probabilities of moving to higher and lower dimensional spaces. Graphical and numerical techniques are used to compare different updating schemes. The methodology is illustrated by applying it to both simulated and real data sets and the results for the Bayesian model selection and parameter estimation procedures are compared with the classical model selection criteria and maximum likelihood estimation.

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