Critical values for multiple structural change tests

TLDR: In this paper, the authors considered the problem of testing for multiple structural changes under very general conditions on the data and the errors: they considered a type test for the null hypothesis of no change vs. a pre-specified number of changes and also vs. the alternative hypothesis of I + 1 changes.

Abstract: Bai and Perron (1998), henceforth BP, considered estimating multiple structural changes in a linear model. The results are obtained under a general framework of partial structural changes which allows a subset of the parameters not to change.1 Methods to efficiently compute estimates are discussed in Bai and Perron (2003). BP also addressed the problem of testing for multiple structural changes under very general conditions on the data and the errors: they considered a type test for the null hypothesis of no change vs. a pre-specified number of changes and also vs. an alternative of an arbitrary number of changes (up to some maximum), as well as a procedure that allows one to test the null hypothesis of, say, I changes, vs. the alternative hypothesis of I + 1 changes. The latter is particularly useful in that it allows a specific to general modeling strategy to consistently determine the appropriate number of changes in the data. The tests can be constructed allowing different serial correlation in the errors, different distribution for the data and the errors across segments or imposing a common structure.