Approximate p-Values of Certain Tests Involving Hypotheses About Multiple Breaks

Abstract We provide formulae for calculating approximate p-values for the non-standard asymptotic null distributions of a variety of tests used for detecting multiple structural change in a wide range of models. Our approximations are based on simulated quantiles obtained from 100,000 replications, and the latter are more accurate than the quantiles reported in the literature by increasing the number of replications by a factor of 10. The p-value response surfaces are approximated using a parametric method proposed by Hansen and their use is illustrated with an example. Using our p-value response surfaces, it is shown that the use of Bai and Perron’s response surfaces for the critical values of these tests can lead to misleading inferences, and thus should be used with extreme caution.