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About the article
Published Online: 2013-03-15
Published in Print: 2013-07-01
The error must also satisfy certain other conditions detailed in the sources mentioned below.
If p=0 then all parameters are regime specific and the model is said to exhibit pure structural change.
It should be noted that these limiting distributions only apply for the statistics based on FT(λ1,…,λk;q) if the regression error ut is homoscedastic and serially uncorrelated. If the errors are heteroscedastic and/or serially correlated then the same limiting distributions hold for the analogous functions of Wald statistics that satisfactorily account for the error structure; see Bai and Perron (1998) for further details.
Such large values of ε are reported because Andrews (1993) allows for asymmetric trimming.
This methodology has also been employed by Sen and Hall (1999) for the distributions of their overidentifying restrictions test (OT) and by Sen (1999) for the Ghysels, Guay, and Hall’s (1997) predictive test.
From the case of q=1, it can be seen that this case occurs for k=9. Further investigation reveals the main source of the distortion is Bai and Perron’s (2003b) response surface: the appropriate critical value reported in Bai and Perron (1998) is 5.20 which translates, using our response surfaces, to a p-value of 0.0758; the critical value predicted by Bai and Perron’s (2003b) response surface is 3.8023. In contrast, our simulations (based on an enhanced design) yield a critical value of 5.4210 for which our response surface gives a p-value of 0.05006.
In the original version of this paper, we restricted attention to q=1,5,10 but, given the nature of the results for those cases, a referee conjectured Bai and Perron’s (2003b) response surfaces would work well for cases q>10. While natural given results for q=1, 5, 10, this conjecture is erroneous as our results demonstrate. We therefore included these cases to avoid the reader making the same mistake. We attribute the inaccuracy of Bai and Perron’s (2003b) response surfaces to these cases to the fact that the surfaces were calculated using cases for which q≤10 only.
For completeness, we note that we performed similar calculations for ε=0.10,0.15,0.20,0.25 for q=1,5,10. The distortions are smaller than those reported for ε=0.05 but are nevertheless non-trivial in a number of circumstances. These results are available from the authors upon request.