Least-squares cross-wavelet analysis and its applications in geophysical time series

The least-squares wavelet analysis, an alternative to the classical wavelet analysis, was introduced in order to analyze unequally spaced and non-stationary time series exhibiting components with variable amplitude and frequency over time. There are a few methods such as cross-wavelet transform and wavelet coherence that can analyze two time series together. However, these methods cannot generally be used to analyze unequally spaced and non-stationary time series with associated covariance matrices that may have trends and/or datum shifts. A new method of analyzing two time series together, namely the least-squares cross-wavelet analysis, is developed and applied to study the disturbances in the gravitational gradients observed by GOCE satellite that arise from plasma flow in the ionosphere represented by Poynting flux. The proposed method also shows its outstanding performance on the Westford-Wettzell very long baseline interferometry baseline length and temperature series.