Change Detection in Time Series Using the Maximal Overlap Discrete Wavelet Transform

The problem of change detection of time series with abrupt and smooth changes in the spectral characteristics is addressed. We first review the main characteristics of the discrete wavelet transform and the maximal overlap discrete wavelet transform. An algorithm for sequential change detection in time series is then reported based on the maximal overlap discrete wavelet transform and Bayesian analysis. The wavelet-based algorithm checks the wavelet coefficients across resolution levels and locates smooth and abrupt changes in the spectral characteristics in the given time series by using the wavelet coefficients at these levels. Simulation results demonstrate the good detection properties of the proposed algorithm when compared with previous reported algorithms, and also indicate that the quadratic spline and least-asymmetric wavelets have less amount of shift in position after wavelet decomposition and therefore an alignment of events to be detected in a multi-resolution analysis with respect to the original time series is obtained. Keywords— wavelets, wavelet transforms, change detection, time series.