Abstract
We develop a general Bayesian semiparametric change-point model in which separate groups of structural parameters (for example, location and dispersion parameters) can each follow a separate multiple change-point process, driven by time-dependent transition matrices among the latent regimes. The distribution of the observations within regimes is unknown and given by a Dirichlet process mixture prior. The properties of the proposed model are studied theoretically through the analysis of inter-arrival times and of the number of change-points in a given time interval. The prior-posterior analysis by Markov chain Monte Carlo techniques is developed on a forward-backward algorithm for sampling the various regime indicators. Analysis with simulated data under various scenarios and an application to short-term interest rates are used to show the generality and usefulness of the proposed model.
Highlights
Multiple change-point models allow for changes of model distributions at multiple, unknown, time points
We differ from the other approaches, since we model the prior distributions of the structural parameters as Dirichlet process (DP), letting the state indicator of the regimes follow Chib (1998)
We have introduced a new Bayesian semiparametric change-point model with various attractive features, to robustly analyze time series with unknown locations and number of multivariate change-points
Summary
Multiple change-point models allow for changes of model distributions at multiple, unknown, time points. 728 Semiparametric Multivariate and Multiple Change-Point Modeling takes advantage of the widely used formulation of Chib (1998), where the change-point modeling is in terms of a latent discrete state variable that follows a unidirectional Markov process and indicates the regime from which a particular observation has been drawn. The Dirichlet concentration parameters are state-dependent and inferred from the data, so that the extent to which estimates deviate from the base parametric measures can differ among groups of structural parameters We refer to this model as a Bayesian semiparametric multivariate multiple change-point model. We differ from the other approaches, since we model the prior distributions of the structural parameters as DPs, letting the state indicator of the regimes follow Chib (1998) This allows for greater parsimony, while still permitting recurrence of regimes and an unknown number of regime changes. Available upon request, have been written in the R programming language and run on a PC with core i7-7500U CPU @ 2.70GHz
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