Constrained forecasting in autoregressive time series models: A Bayesian analysis

A Bayesian approach is used to derive constrained and unconstrained forecasts in an autoregressive time series model. Both are obtained by formulating an AR(p) model in such a way that it is possible to compute numerically the predictive distribution for any number of forecasts. The types of constraints considered are that a linear combination of the forecasts equals a given value. This kind of restriction is applied to forecasting quarterly values whose sum must be equal to a given annual value. Constrained forecasts are generated by conditioning on the predictive distribution of unconstrained forecasts. The procedures are applied to the Quarterly GNP of Mexico, to a simulated series from an AR(4) process and to the Quarterly Unemployment Rate for the United States.