Bayesian Nonparametric State Space Models via Mixture Process of Products of Dirichlet Processes

Parametrically specified measurement and transition equations in State Space Models (SSM) are a source of bias in case of a mismatch between parametric assumptions and reality. The mixture process of products of Dirichlet processes (MPDP) is proposed as a flexible modeling framework for SSMs when there is uncertainty on the distributional assumption in the measurement equation. It is shown that the MPDP prior can approximate any prior belief and that the true parametric SSM can be approximated arbitrarily well by a nonparametric SSM with MPDP prior on the conditional distribution of the observations. An efficient estimation algorithm is designed for posterior sampling, with minimum additional computational effort relative to parametric models. Two simulated exercises on Gaussian Kalman Filtering and Hidden Markov Models, and an empirical application for regime shifts in interest rates, show the better performance of the proposed approach when compared to parametric SSMs.