We propose a novel Bayesian method for dynamic regression models where both the values of the regression coefficients and the importance of the variables are allowed to change over time. The parsimony of the model is important for good forecasting performance and we develop a prior which allows the shrinkage of the regression co-efficients to suitably change over time. An efficient MCMC method for computation is described. The new method is then applied to two forecasting problems in econometrics: equity premium prediction and inflation forecasting. The results show that this method outperforms current competing Bayesian methods
