Subsample scan test for multiple breaks based on self-normalization

The self-normalization of Shao and Zhang and subsample scan method of Yau and Zhao are combined to produce a test S_N for testing breaks for time series data. Unlike the original break test based on self-normalization of Shao and Zhang, the proposed test has power against canceling multiple breaks. The proposed test has several advantages over an existing test T_N of Zhang and Lavitas designed for the same purpose of detecting canceling multiple breaks: having no computational burden issue; having stabler size; having no need for specification of a trimming parameter. Comparison is also made with the recent test U_N by Schmidt for mean break and by Schmidt et al. for variance break based on U-statistics and shows better size of S_N than U_N for serially correlated samples but worse power of S_N than U_N. Unlike U_N, S_N is a general purpose test which can be used for testing break in any parameter, for example, correlation, under some weak conditions. These advantages recommend us the proposed test S_N as a practical alternative to T_N and U_N in spite of some disadvantages of smaller power and requiring specification of a parameter for the number of windows.