Wavelet coherence :|analysis of time series and exploration towards fault detection

Abstract

Wavelet Coherence Analysis (WCA) is a tool for depicting degree of coherency and phase differences between binary time series. The advantages of WCA are the capability to cope with non-stationary time series and to monitor the time- and frequency-domain information collectively. In this thesis, commonly used WCA software toolboxes were comparatively evaluated and a hybrid MATLAB code was developed. WCA was used to elucidate possible coherency and lead-lag relationships between binary time series. Data pertaining to engineering and economics were used. Studies with CAB (Chemical Activity Barometer) and IPI (US Industrial Production Index) disclosed the power of WCA in explicating and interpreting the coherency and lead-lag relationships hidden between these series and confirmed the claims made by ACC (American Chemistry Council) that the CAB leads IPI. Additionally, it was shown that at US Business Cycle periods (0.5 to two years), the troughs (ends of economic recessions) observed with WCA of CAB and IPI lead the troughs claimed by ACC. WCA supports that CAB is a leading indicator of the US economy, especially during economic recessions between 1945 and 2007. Comparative studies demonstrated that working with detrended series increased resolution of WCA while working with moving-averaged series distorted WCA due to introduction of artificial lags in averaging. WCA application to yearly CAB and Chemical Engineering Plant Cost Index (CEPCI) and yearly IPI and CEPCI pairs exhibited that it was not possible to decide whether CEPCI is a leading indicator for the US economy or not. Furthermore, for the first time in literature, WCA was used as a tool for Fault Detection (FD). Fault containing synthetic time series along with unfaulty one were used to evaluate the potential of WCA in FD. It was shown that WCA can detect faults quickly and is a viable tool for FD, change point identification, and template matching tasks.