Detecting structural changes using wavelets

- We develop a wavelet structural break test.
- We establish limiting distribution of the test.
- We analyze the size and power properties of the test in a simulation study.
- We show that the test has a reasonable size and substantial power.
- The power is significantly higher compared to alternatives when breaks are multiple.

We propose a powerful wavelet method to identify structural breaks in the mean of a process. If there is a structural change in the mean, the sum of the squared scaling coefficients absorbs more variation, leading to unequal weights for the variances of the wavelet and scaling coefficients. We use this feature of wavelets to design a statistical test for changes in the mean of an independently distributed process. We establish the limiting null distribution of our test and demonstrate that our test has good empirical size and substantive power relative to the existing alternatives especially for multiple breaks.