Bayesian inference and state number determination for hidden Markov models: an application to the information content of the yield curve about inflation

This paper is concerned with Bayesian inference in hidden Markov models. Focusing on switching regression models, we propose a new methodology that delivers a joint estimation of the parameters and the number of regimes that have actually appeared in the studied sample. The only prior information that is required on the latter quantity is an upper bound. We implement a particle filter algorithm to compute the corresponding estimates. Applying this methodology to the information content of the yield curve regarding future inflation in four OECD countries, we show that the predictive content for given country and combination of maturities is subject to regime switching.