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gmwmx Overview

The gmwmx R package implement the Generalized Method of Wavelet Moments with Exogenous Inputs estimator (GMWMX) introduced in Cucci, D. A., Voirol, L., Kermarrec, G., Montillet, J. P., and Guerrier, S. (2022) <arXiv:2206.09668> and provides functions to estimate times series models that can be expressed as linear models with correlated residuals. Moreover, the gmwmx package provides tools to compare and analyze estimated models and methods to easily compare results with the Maximum Likelihood Estimator (MLE) implemented in Hector, allowing to replicate the examples and simulations considered in Cucci, D. A., Voirol, L., Kermarrec, G., Montillet, J. P., and Guerrier, S. (2022) <arXiv:2206.09668>. In particular, this package implements a statistical inference framework for the functional and stochastic parameters of models such as those used to model Global Navigation Satellite System (GNSS) observations, enabling the comparison of the proposed method to the standard MLE estimates implemented in Hector.

Find the package vignettes and user’s manual at the package website.

Below are instructions on how to install and make use of the gmwmx package.

Installation Instructions

The gmwmx 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 gmwmx package with:


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/Update the package from GitHub

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

External dependencies


In order to runs successfully functions that execute Hector, we assume that Hector is installed and available in the PATH of the installation where these functions are called. More precisely, when running either estimate_hector(), remove_outliers_hector(), PBO_get_station() or PBO_get_offsets(), we assume that Hector’s binaries executable estimatetrend, removeoutliers and date2mjd are located in a folder available in the PATH by R.

In order to make sure that these functions are available in the PATH, you can run Sys.getenv("PATH") and ensure that the directory that contains the executable binaries of Hector is listed in the PATH.

For Linux users that are on distributions supported by Hector, this can be easily done by:

  1. Downloading Hector’s binaries for the corresponding OS here.
  2. Extracting the downloaded executable binaries and saving them in a folder, say $HOME/app/hector/bin.
  3. Adding this folder to the system-wide PATH environment variable by modifying /etc/environment.
  4. Ensuring that the corresponding folder is accessible by R with Sys.getenv("PATH") after running the script and reassigning the new PATH to the PATH environment variable with . /etc/environment or equivalently with source /etc/environment.
> Sys.getenv("PATH")
[1] "$HOME/app/hector/bin:..."

External R libraries

The gmwmx 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.


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


Cucci, D.A., Voirol, L., Kermarrec, G., Montillet, J.P. and Guerrier, S., 2022. The Generalized Method of Wavelet Moments with Exogenous Inputs: a Fast Approach for the Analysis of GNSS Position Time Series. arXiv preprint arXiv:2206.09668.

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.