Structural Change and the Problem of Phantom Break Locations

It is well known, in structural break problems, that it is much easier to detect the existence of a break in a data set than to determine the location of such a break in the sample span. This paper investigates why, in the context of Gaussian linear regressions, using a decision theory framework. The nub of the problem, even for moderately sized breaks, is that the posterior probability distribution of the possible break points is usually not very informative about the true break location. The information content is measured here by a proper scoring rule. Hence, even a locally optimal break location procedure, as introduced here, is ineffective. In the regression context, it turns out to be quite common, indeed the norm, for break location procedures to misidentify the true break position up to 100 per cent of the time. Unfortunately too, the magnitude of the difference between the misidentified and true break locations is usually not small.