Constrained Forecasts in Arma Models: a Bayesian Approach

A Bayesian approach is developed to generate constrained and unconstrained forecasts in autoregressive-moving average time series models. Both are calculated by formulating the ARMA(p,q) model in such a way that it is possible to numerically compute the predictive distribution for any number of forecasts as in de Alba (1993). We obtain the posterior distribution of the parameters via Gibbs sampling and the pre-dictive distribution using Monte Carlo integration. The kind of constraints used are that a linear combination of the forecasts equals a given value. The constrained forecasts are obtained by conditioning in the predictive distribution of the unconstrained forecasts. The results are applied to a series of quarterly innation in Mexico.