![]() ![]() ![]() The first main aim of this paper is to quantify these size distortions for structural break tests that are applied conditional on large deviations being observed in the data. Of course, such tests are exclusively constructed to hold size unconditionally and, hence, suffer from size distortions if applied otherwise. Hence, any change point test, if it is to be valid, needs to hold size conditional on having looked at the data. However, one problem with the recommendation to look for ‘any apparent sharp changes in behavior’ is that the decision to apply the structural break test has been informed by the data. To avoid such misleading test results, applying a formal structural break test is typically recommended as a pre-step to the actual statistical analysis of the data. For instance, Xu ( 2015) shows that if a structural break in the error variances is ignored, standard tests for the the constancy of regression coefficients suffer from size distortions-even asymptotically. 2013 Demetrescu and Hanck 2013 Harvey et al. If such a change is present in the data, yet is ignored in the subsequent analysis, the conclusions drawn from the data may be invalid (see, e.g., Baltagi et al. ![]() For instance, Brockwell and Davis ( 2016, p. 12) recommend time series plots to check whether there are ‘any apparent sharp changes in behavior’. The importance of plotting the data as a first step of a statistical analysis is stressed in numerous textbooks (e.g., Ruppert and Matteson 2015 Brockwell and Davis 2016). ![]()
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