We propose a wavelet based approach for detecting mean break in a time series. Two types of test statistics are derived using the cumulative sum (CUSUM) of wavelet and scaling coefficients computed from the maximal-overlapped discrete wavelet transform (MODWT). We then apply appropriate self-normalizer for each statistic and avoid the estimation of the long run variance. Under moments and mixing conditions, the test statistics satisfy the functional central limit theorem (FCLT) for a broad class of time series models. Good power performance is reported in simulations. We illustrate its usefulness by considering an important series, the Northern Hemisphere Temperature.

time series, mean break, CUSUM test, wavelet transform.