Analysis of correlated random effects: linear model with two random components

Linear regression models with two random components, one of which is time correlated, are analysed from a Bayesian viewpoint. The problem of making inferences about the parameters when the time correlated component is stationary is discussed. Necessary modifications needed for nonstationary and explosive models are indicated. The analysis is illustrated by a numerical example showing that the time series component of the data can exert a strong influence in determining the posterior distribution of the regression coefficients. Finally, the case of several linear models is considered and a possible application to seasonal series is indicated.