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.
Ghaderpour, Ebrahim, and Spiros D. Pagiatakis. “Least-Squares Wavelet Analysis of Unequally Spaced and Non-Stationary Time Series and Its Applications.” Mathematical Geosciences, vol. 49, no. 7, Springer Nature, June 2017, pp. 819–44, doi:10.1007/s11004-017-9691-0.
Ghaderpour, Ebrahim, and Spiros D. Pagiatakis. “Least-Squares Wavelet Analysis of Unequally Spaced and Non-Stationary Time Series and Its Applications.” Mathematical Geosciences, vol. 49, no. 7, Springer Nature, June 2017, pp. 819–44, doi:10.1007/s11004-017-9691-0.
APA
Ghaderpour, E., & Pagiatakis, S. D. (2017). Least-Squares Wavelet Analysis of Unequally Spaced and Non-stationary Time Series and Its Applications. Mathematical Geosciences, 49(7), 819–844. Springer Nature. Retrieved from https://doi.org/10.1007%2Fs11004-017-9691-0
BibTeX
@article{Ghaderpour_2017,
doi = {10.1007/s11004-017-9691-0},
url = {https://doi.org/10.1007%2Fs11004-017-9691-0},
year = 2017,
month = {jun},
publisher = {Springer Nature},
volume = {49},
number = {7},
pages = {819--844},
author = {Ebrahim Ghaderpour and Spiros D. Pagiatakis},
title = {Least-Squares Wavelet Analysis of Unequally Spaced and Non-stationary Time Series and Its Applications},
journal = {Mathematical Geosciences}
}
Ghaderpour, Ebrahim, et al. “Antileakage Least-Squares Spectral Analysis for Seismic Data Regularization and Random Noise Attenuation.” GEOPHYSICS, vol. 83, no. 3, Society of Exploration Geophysicists, Mar. 2018, pp. V157–V170, doi:10.1190/geo2017-0284.1.
Ghaderpour, Ebrahim, et al. “Antileakage Least-Squares Spectral Analysis for Seismic Data Regularization and Random Noise Attenuation.” GEOPHYSICS, vol. 83, no. 3, Society of Exploration Geophysicists, Mar. 2018, pp. V157–V170, doi:10.1190/geo2017-0284.1.
APA
Ghaderpour, E., Liao, W., & Lamoureux, M. P. (2018). Antileakage least-squares spectral analysis for seismic data regularization and random noise attenuation. GEOPHYSICS, 83(3), V157–V170. Society of Exploration Geophysicists. Retrieved from https://doi.org/10.1190%2Fgeo2017-0284.1
BibTeX
@article{Ghaderpour_2018,
doi = {10.1190/geo2017-0284.1},
url = {https://doi.org/10.1190%2Fgeo2017-0284.1},
year = 2018,
month = {mar},
publisher = {Society of Exploration Geophysicists},
volume = {83},
number = {3},
pages = {V157--V170},
author = {Ebrahim Ghaderpour and Wenyuan Liao and Michael P. Lamoureux},
title = {Antileakage least-squares spectral analysis for seismic data regularization and random noise attenuation},
journal = {{GEOPHYSICS}}
}
Ghaderpour, Ebrahim, et al. “Least-Squares Cross-Wavelet Analysis and Its Applications in Geophysical Time Series.” Journal of Geodesy, vol. 92, no. 10, Springer Nature, May 2018, pp. 1223–36, doi:10.1007/s00190-018-1156-9.
Ghaderpour, Ebrahim, et al. “Least-Squares Cross-Wavelet Analysis and Its Applications in Geophysical Time Series.” Journal of Geodesy, vol. 92, no. 10, Springer Nature, May 2018, pp. 1223–36, doi:10.1007/s00190-018-1156-9.
APA
Ghaderpour, E., Ince, E. S., & Pagiatakis, S. D. (2018). Least-squares cross-wavelet analysis and its applications in geophysical time series. Journal of Geodesy, 92(10), 1223–1236. Springer Nature. Retrieved from https://doi.org/10.1007%2Fs00190-018-1156-9
BibTeX
@article{Ghaderpour_2018,
doi = {10.1007/s00190-018-1156-9},
url = {https://doi.org/10.1007%2Fs00190-018-1156-9},
year = 2018,
month = {may},
publisher = {Springer Nature},
volume = {92},
number = {10},
pages = {1223--1236},
author = {Ebrahim Ghaderpour and E. Sinem Ince and Spiros D. Pagiatakis},
title = {Least-squares cross-wavelet analysis and its applications in geophysical time series},
journal = {Journal of Geodesy}
}
Ghaderpour, Ebrahim, and Spiros D. Pagiatakis. “LSWAVE: a MATLAB Software for the Least-Squares Wavelet and Cross-Wavelet Analyses.” GPS Solutions, vol. 23, no. 2, Springer Nature, Mar. 2019, doi:10.1007/s10291-019-0841-3.
Ghaderpour, Ebrahim, and Spiros D. Pagiatakis. “LSWAVE: a MATLAB Software for the Least-Squares Wavelet and Cross-Wavelet Analyses.” GPS Solutions, vol. 23, no. 2, Springer Nature, Mar. 2019, doi:10.1007/s10291-019-0841-3.
APA
Ghaderpour, E., & Pagiatakis, S. D. (2019). LSWAVE: a MATLAB software for the least-squares wavelet and cross-wavelet analyses. GPS Solutions, 23(2). Springer Nature. Retrieved from https://doi.org/10.1007%2Fs10291-019-0841-3
BibTeX
@article{Ghaderpour_2019,
doi = {10.1007/s10291-019-0841-3},
url = {https://doi.org/10.1007%2Fs10291-019-0841-3},
year = 2019,
month = {mar},
publisher = {Springer Nature},
volume = {23},
number = {2},
author = {Ebrahim Ghaderpour and Spiros D. Pagiatakis},
title = {{LSWAVE}: a {MATLAB} software for the least-squares wavelet and cross-wavelet analyses},
journal = {{GPS} Solutions}
}