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

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## Abstract

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.

## Keywords

Least-squares spectral analysis Antileakage least-squares spectral analysis GPS time series analysis Least-squares wavelet analysis Least-squares cross-spectral analysis Least-squares cross-wavelet analysis## Notes

### Acknowledgements

This research has been financially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and partially by the Carbon Management Canada (CMC) National Centre of Excellence (Canada).

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