Selection of mother wavelet for bivariate wavelet analysis

This study explores the effect of mother wavelet in the bivariate wavelet analysis. A total of four mother wavelets (Bump, Mexican hat, Morlet, and Paul) which are frequently used in the related studies is selected. These mother wavelets are applied to several bivariate time series like white noise and sine curves with different periods, whose results are then compared and evaluated. Additionally, two real time series such as the arctic oscillation index (AOI) and the southern oscillation index (SOI) are analyzed to check if the results in the analysis of generated time series are consistent with those in the analysis of real time series. The results are summarized as follows. First, the Bump and Morlet mother wavelets are found to provide well-matched results with the theoretical predictions. On the other hand, the Mexican hat and Paul mother wavelets show rather short-periodic and long-periodic fluctuations, respectively. Second, the Mexican hat and Paul mother wavelets show rather high scale intervention, but rather small in the application of the Bump and Morlet mother wavelets. The so-called co-movement can be well detected in the application of Morlet and Paul mother wavelets. Especially, the Morlet mother wavelet clearly shows this characteristic. Based on these findings, it can be concluded that the Morlet mother wavelet can be a soft option in the bivariate wavelet analysis. Finally, the bivariate wavelet analysis of AOI and SOI data shows that their periodic components of about 2-4 years co-move regularly every about 20 years.