LSWAVE: a MATLAB software for the least-squares wavelet and cross-wavelet analyses

The least-squares wavelet analysis (LSWA) is a robust method of analyzing any type of time/data series without the need for editing and preprocessing of the original series. The LSWA can rigorously analyze any non-stationary and equally/unequally spaced series with an associated covariance matrix that may have trends and/or datum shifts. The least-squares cross-wavelet analysis complements the LSWA in the study of the coherency and phase differences of two series of any type. A MATLAB software package including a graphical user interface is developed for these methods to aid researchers in analyzing pairs of series. The package also includes the least-squares spectral analysis, the antileakage least-squares spectral analysis, and the least-squares cross-spectral analysis to further help researchers study the components of interest in a series. We demonstrate the steps that users need to take for a successful analysis using three examples: two synthetic time series, and a Global Positioning System time series.