Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models

Abstract

Time series subject to parameter shifts of random magnitude and timing are commonly modeled with a change-point approach using Chib's (1998) algorithm to draw the break dates. We outline some advantages of an alternative approach in which breaks come through mixture distributions in state innovations, and for which the sampler of Gerlach, Carter and Kohn (2000) allows reliable and efficient inference. We show how the same sampler can be used to (i) model shifts in variance that occur independently of shifts in other parameters (ii) draw the break dates in O(n) rather than O(n³) operations in the change-point model of Koop and Potter (2004b), the most general to date. Finally, we introduce to the time series literature the concept of adaptive Metropolis-Hastings sampling for discrete latent variable models. We develop an easily implemented adaptive algorithm that improves on Gerlach et al. (2000) and promises to significantly reduce computing time in a variety of problems including mixture innovation, change-point, regime-switching, and outlier detection. The efficiency gains on two models for U.S. inflation and real interest rates are 257% and 341%.