On the usability of the fluctuation test statistic to identify multiple cointegration break points

The fluctuation test suggested by Hansen and Johansen [ Some tests for parameter constancy in cointegrated VAR models , Econometrics J. 2 (1999), pp. 306--333] intends to distinguish between the presence of zero and one break in cointegration relations. In this article, we provide evidence by Monte Carlo simulations that it also serves as a graphical device to detect even multiple break locations. It suffices to consider a simplified and easy-to-implement version of the original fluctuation test. Its break detection performance depends on the sign of change in cointegration parameters and the break height. The sign issue can be approached successfully by a backward application of the test statistic. If breaks are observable, the break locations are detected at the true location on average. We apply the graphical procedure to assess the cointegration of bond yields of Spain, Italy and Portugal with German yields for the period 1995--2013 which is surprisingly supported by the trace test. However, the recursive cointegration approach shows that a stable relationship with German yields is only present for sub-periods between the introduction of the Euro and the global financial crisis which is in line with expectations. The statistical robustness of these results is supported by a forward and backward application of the cointegration breakdown test by Andrews and Kim [ Tests for cointegration breakdown over a short time period , J. Bus. Econom. Stat. 24 (2006), pp. 379--394].