BAYESIAN CONSISTENCY FOR STATIONARY MODELS

In this paper, we provide a Doob-style consistency theorem for stationary models+ Many applications involving Bayesian inference deal with non independent and identically distributed data, in particular, with stationary data+ However, for such models, there is still a theoretical gap to be filled regarding the asymptotic properties of Bayesian procedures+ The primary goal to be achieved is establishing consistency of the sequence of posterior distributions+ Here we provide an answer to the problem+ Bayesian methods have recently gained growing popularity in economic modeling, thus implying the timeliness of the present paper+ Indeed, we secure Bayesian procedures against possible inconsistencies+ No results of such a generality are known up to now+