Bayesian and Non-Bayesian Analysis of Switching Regressions and of Random Coefficient Regression Models

Abstract Quandt 20 analyzed the problem of discontinuous shifts in regression regimes at unknown points in the data series. We note that Quandt's statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method based on a proper prior distribution of the unknown parameters yields sensible results. However, the exact evaluation of the posterior distribution is unusually burdensome and cannot be simplified even in large samples. To avoid this difficulty, we suggest an alternative formulation and provide an approximate Bayesian solution. In this alternative formulation, the coefficient vectors are treated as random drawings from a continuous multivariate distribution.