On the classification of time series and cross wavelet phase variance - Pienaar, Marc (Department of Electrical Engineering, 2017)
The continuous wavelet transform (CWT) is arguably one of the best tools to explore underlying characteristic features of time series data. Its application in large time series classification experiments, however, has been severely limited due to the large amount of redundant associated information. By extending the capabilities of the CWT to perform cross wavelet analysis (CWA), common frequency behaviour between two time series is highlighted, and the potential to extract amplitude modulated (AM) and frequency modulation (FM) characteristics in an automated way is possible. Characterisation of AM is relatively straightforward and can be resolved by any number of Euclidean based techniques in both the time and frequency domains. FM on the other hand, is somewhat more difficult as it transcends multiple wavelet scales. In this study, linear combinations of scales are used to extract both AM similarity (derived from global wavelet power spectra) and FM coherency, using a new method developed called cross wavelet phase variance (CWPV). The methodology is applied to large scale classification problems (using benchmark time series), in which the method clearly outperforms other common distance-based measures. Lastly, the approach provides a powerful framework in which AM and FM characteristics common between time series can be explicitly mapped to their corresponding scales, and with some initial optimisation, can be applied to any classification problem.