Alternative regime switching models for forecasting inflation

US inflation appears to undergo shifts in its mean level and variability. We evaluate the performance of three useful models for capturing such shifts. The models studied are the Markov switching models, state space models with heavy-tailed errors, and state space models with compound error distributions. Our study shows that all three models have very similar performance when evaluated in terms of the mean squared or mean absolute forecast errors. However, the latter two models are considerably more parsimonious, and easily beat the more profligately parameterized Markov switching models in terms of model selection criteria, such as the AIC or the SBC. Thus, these may serve as useful continuous alternatives to the popular discrete Markov switching models for capturing shifts in time series.