A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change

A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models

“…It is also a partial-sums type test for which only a model restricted to satisfy the null hypothesis of no change is used. It has been shown that tests based on such features have serious non-monotonic power problems; see, e.g., Deng and Perron (2008), Kim and Perron (2009), Perron and Yamamoto (2012). In the context of structural change tests, one should be skeptical of the use of some local asymptotic frameworks whereby the breaks are local to zero to devise testing procedures.…”

“…They showed LM-based procedures to be ine¢ cient. Deng and Perron (2008) studied the power functions of the CUSUM and CUSUM of squares tests and showed that the relative properties of those two tests can be di¤erent from what the local asymptotic framework used by Ploberger and Krämer (1990) suggested when the errors are serially correlated or a lagged dependent variable is included as a regressor in the model. Perron and Yamamoto (2012) considered the so-called optimal qLL test of Elliott and Müller's (2006) for general parameter variations in which a local asymptotic framework is also adopted.…”

Testing for factor loading structural change under common breaks

“…Subsequent literature carries out asymptotic analyses of the power problem for the case of CUSUM and CUSUM squared tests (Deng and Perron, 2006), the tests proposed by Andrews (1993) and Andrews and Ploberger (1994) (Kim and Perron, 2009), and Elliott and M• uller's (2006) d qLL test (Perron and Yamamoto, 2013). In these cases, one of the important sources of nonmonotonic power is found to be the problem of identifying the persistence parameter and structural change in the conditional mean of the model.…”

Improving the finite sample performance of tests for a shift in mean

“…As explained in Crainiceanu and Vogelsang (2007) and Deng and Perron (2008), this test suffers from the non-monotonic power problem because the long-run variance is estimated under the null hypothesis of no break. In order to avoid this problem, we again consider estimating the long-run variance under the alternative of a one-time break.…”

“…This problem was investigated by Vogelsang (1999), Crainiceanu and Vogelsang (2007), Deng and Perron (2008), and Perron and Yamamoto (2014). The reason for this problem is that the long-run variance estimator takes significantly large values as the magnitude of the break increases.…”