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 flrst review the main characteristics of the dis- crete wavelet transform and the maximal over- lap 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 anal- ysis. The wavelet-based algorithm checks the wavelet coe-cients across resolution levels and locates smooth and abrupt changes in the spec- tral characteristics in the given time series by using the wavelet coe-cients at these levels. Simulation results demonstrate the good de- tection properties of the proposed algorithm when compared with previous reported algo- rithms, and also indicate that the quadratic spline and least-asymmetric wavelets have less amount of shift in position after wavelet decom- position and therefore an alignment of events to be detected in a multi-resolution analysis with respect to the original time series is obtained.

[1]  Vicente Alarcón Aquino.  Anomaly detection and prediction in communication networks using wavelet transforms , 2003 .

[2]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[3]  V. Alarcon-Aquino,et al.  Multiresolution FIR neural-network-based learning algorithm applied to network traffic prediction , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[4]  Dzulkifli Mohamad,et al.  Segmentation of Malay Syllables in Connected Digit Speech Using Statistical Approach , 2007 .

[5]  Vicente Alarcon-Aquino,et al.  Multi-Sensor Fusion System Using Wavelet Based Detection Algorithm Applied to Network Monitoring , 2002 .

[6]  F. Gustafsson.  The marginalized likelihood ratio test for detecting abrupt changes , 1996, IEEE Trans. Autom. Control..

[7]  Bhavik R. Bakshi,et al.  Multiscale analysis and modeling using wavelets , 1999 .

[8]  Ulrich Appel,et al.  Adaptive sequential segmentation of piecewise stationary time series , 1983, Inf. Sci..

[9]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[10]  V. Alarcón-Aquino,et al.  Anomaly detection in communication networks using wavelets , 2001 .

[11]  Tzung-Pei Hong,et al.  Segmentation of Time Series by the Clustering and Genetic Algorithms , 2006, Sixth IEEE International Conference on Data Mining - Workshops (ICDMW'06).

[12]  Michael R. Chernick,et al.  Wavelet Methods for Time Series Analysis , 2001, Technometrics.

[13]  Jacques Duchêne,et al.  Detection and classification of multiple events in piecewise stationary signals: Comparison between autoregressive and multiscale approaches , 1999, Signal Process..

[14]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[15]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .