Detection of Join Point in Regression Models

A Bayesian predictive density for the mean squared errors of post-sample forecasts is derived within the linear regression framework. The kernel of the predictive density is an F distribution. In the process of deriving the predictive density, we use a degenerate hyperbolic function to express the distribution of quadratic forms in normal variables. The Bayesian predictive density is then used to detect a join point by the highest posterior density interval criterion. Numerical examples are given to compare the Bayesian predictive density procedure with the maximum likelihood and Bayesian posterior density procedures for detecting the join point. When the join point is at either the beginning or ending edge of the sample period, the Bayesian predictive density procedure detects the join point whereas the maximum likelihood and Bayesian posterior density procedures cannot.