The one-step forecast intervals for ARMA models via a random coefficient approach and a Bayesian approach are investigated. We prove analytically that the point forecast and the forecast variation via the Bayesian approach can be represented as formulae similar to those via the random coefficient approach. The numerical difference relies upon the proper estimates for unknown quantities which are substituted for each approach. Especially when the improper prior density is applied, the point forecast for the Bayesian approach is exactly equal to the one via the random coefficient approach. Moreover, three sets of real data are used to compare the precision of the one-step forecasts from both approaches. The numerical results indicate that essentially there is little if any difference between the two approaches.
