gmwmx2 Overview

The gmwmx2 R package implements the Wavelet Moment Regression (WAMORE) inference framework presented in Voirol, L., Xu, H., Zhang, Y., Insolia, L., Molinari, R. and Guerrier, S. (2026). WAMORE enables computationally efficient estimation and inference for large-scale regression problems with dependent errors, including settings with missing data.

The package supports the joint estimation of (i) functional or structural parameters, (ii) stochastic parameters characterizing the dependence structure of the errors, and (iii) nuisance parameters governing the missingness process.

To illustrate the capabilities of WAMORE, gmwmx2 provides functions to download and visualize Global Navigation Satellite System (GNSS) position time series from the Nevada Geodetic Laboratory. The package enables the estimation of regression models with complex dependence structures represented by composite stochastic processes, with applications including the estimation of tectonic velocities and crustal uplift from GNSS position time series.

The package also provides an implementation of the Generalized Method of Wavelet Moments (GMWM) estimator proposed in Guerrier, S., Skaloud, J., Stebler, Y. and Victoria-Feser, M.-P. (2013).

Detailed examples, vignettes, and the user’s manual are available on the package website.

Below are instructions for installing and using the gmwmx2 package.

Installation Instructions

The gmwmx2 package is available on both CRAN and GitHub. The CRAN version is considered stable while the GitHub version is subject to modifications/updates which may lead to installation problems or broken functions. You can install the stable version of the gmwmx2 package with:

install.packages("gmwmx2")

For users who are interested in having the latest developments, the GitHub version is ideal although more dependencies are required to run a stable version of the package. Most importantly, users must have a (C++) compiler installed on their machine that is compatible with R (e.g. Clang).

# Install dependencies
install.packages(c("devtools"))

# Install/Update the package from GitHub
devtools::install_github("SMAC-Group/gmwmx2")

# Install the package with Vignettes/User Guides 
devtools::install_github("SMAC-Group/gmwmx2", build_vignettes = TRUE)

External R libraries

The gmwmx2 package relies on a limited number of external libraries, but notably on Rcpp and RcppArmadillo which require a C++ compiler for installation, such as for example gcc.

Note on gmwmx2 vs gmwmx

The original gmwmx package was designed to compare estimated parameters obtained from the GMWMX with the ones obtained with the Maximum Likelihood Estimator (MLE) implemented in Hector. This allowed for the replication of examples and simulations discussed in Cucci, D. A., Voirol, L., Kermarrec, G., Montillet, J. P., and Guerrier, S. (2022). However, as we advanced in the methodological and computational development of the GMWMX method, we sought a standalone implementation that did not include Hector. Additionally, many of the new computational techniques and structural improvements would have been challenging to incorporate into the previous gmwmx package. Therefore, we will now exclusively support and develop the gmwmx2 package.

Upcoming features

The gmwmx2 package is currently in the early stages of development. While the supported features are stable, we have numerous additional methods and computational enhancements planned for gradual integration. These include:

• Computational optimization to improve speed
• Support for a wider range of stochastic models to describe the error term
• Support for a wider range of stochastic models to describe the missingness process
• A computationally efficient model selection criterion for stochastic models

License

This source code is released under is the GNU AFFERO GENERAL PUBLIC LICENSE (AGPL) v3.0.

References

Voirol, L., Xu, H., Zhang, Y., Insolia, L., Molinari, R., and Guerrier, S. (2026). Towards Open Science: Monitoring Crustal Deformations in North America. doi:10.48550/arXiv.2607.16264.

Guerrier, S., Skaloud, J., Stebler, Y. and Victoria-Feser, M.P., 2013. Wavelet-variance-based estimation for composite stochastic processes. Journal of the American Statistical Association, 108(503), pp.1021-1030. doi:10.1080/01621459.2013.799920

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