Pairwise Markov Models (PMMs) extend the wellknown Hidden Markov Models (HMMs). Being significantly more general, PMMs enable several types of processing, like Bayesian filtering or smoothing, similar to those used in HMMs. In this paper, we deal with Bayesian forecasting. The aim is to show analytically in the simple stationary Gaussian case that the extent results obtained with HMM can be improved. We complete contributions with a theoretical error study and two real examples we deal with. Experiments show that PMMs-based forecasting can significantly improve HMMs-based ones.