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 SN 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 TN 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 UN by Schmidt for mean break and by Schmidt et al. for variance break based on U-statistics and shows better size of SN than UN for serially correlated samples but worse power of SN than UN. Unlike UN, SN 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 SN as a practical alternative to TN and UN in spite of some disadvantages of smaller power and requiring specification of a parameter for the number of windows.