`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.

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:

`install.packages("gmwmx")`

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

`Hector`

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:

- Downloading
`Hector`

’s binaries for the corresponding OS here. - Extracting the downloaded executable binaries and saving them in a
folder, say
`$HOME/app/hector/bin`

. - Adding this folder to the system-wide
`PATH`

environment variable by modifying`/etc/environment`

. - 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:..."
```

`R`

librariesThe `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.