Combining wavelets and mathematical morphology to detect changes in time series

In this paper, the problem of detecting changes in time series is addressed. First, the time series is decomposed at multiple scales into wavelet coefficients, in order to obtain a preliminary map of the discontinuities/change points. To select only the relevant ones, we here propose a filtering step based on mathematical morphology. To the best of our knowledge, this is the first time that morphological filters are used in combination with the wavelet transform to address the change point detection problem. The methodology has been validated by analyzing a large set of simulated time series featuring a variable number of change points. For a more comprehensive analysis of the performance, different levels of noise have been also added to the original simulated data.