Identification of ARMA Models by Bayesian Methods Applied to Streamflow Data

This work describes a methodology to estimate autoregressive moving average parameters, including both coefficients and model orders, by means of Bayesian inference. In order to solve the integrals involved in the Bayesian methodology, Markov chain Monte Carlo simulation algorithms are employed. The inference of model orders is a formidable task, due to the changes of parameter space dimension involved. To address dimension changes, both Metropolis-Hastings and reversible jump algorithm steps inside a Gibbs sampler are applied. MCMC simulation is also applied to evaluate the predictive capability of the estimated models. The methodology is illustrated with streamflow time series data