Bayesian Inference and Forecasting in the Stationary Bilinear Model

A stationary bilinear (SB) model can be used to describe processes with a time-varying degree of persistence that depends on past shocks. An example of such a process is inflation. This study develops methods for Bayesian inference, model comparison, and forecasting in the SB model. Using monthly U.K. inflation data, we find that the SB model outperforms the random walk and first order autoregressive AR(1) models in terms of root mean squared forecast errors for both the one-step-ahead and the multi-step-ahead out-of-sample forecast. In addition, the SB model is superior to these two models in terms of predictive likelihood for 208 out of 243 forecast observations. In particular, compared with a lower order autoregressive AR model, the SB model is much better at predicting the inflation observations during the financial crisis and immediately after.