Generalized Method of Wavelet Moments (GMWM) is an estimation technique for the parameters of time series models. It uses the wavelet variance in a moment matching approach that makes it particularly suitable for the estimation of certain state-space models.
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Failed to load latest commit information.

Linux Build StatusCRAN RStudio mirror downloadsCRAN_Status_Badge

gmwm R Package

This repository holds the Generalized Method of Wavelet Moments (GMWM) R package. This estimation technique uses the wavelet variance in a moment-matching spirit to estimate parameters of time series models such as ARMA or state-space models. A robust version of the GMWM is also implemented in this package together with a tailored made method for inertial sensors calibration, which typically deals with very large sample sizes.

Below are examples of the capabilities of the gmwm package.

To start, let's generate some data:

## Data generation ##
# Specify model
m = AR1(phi = .98, sigma2 = .01) + WN(sigma2 = 1)

# Generate Data
d = gen_gts(10000, m)

Once we have data, we can see what the wavelet variance looks like for the data with the classical and robust wavelet variances.

# Calculate the classical wavelet variance with the Haar filter
wv.classical = wvar(d)

# Plot the data

# Calculate robust wavelet variance
wv.robust = wvar(d, robust = TRUE, eff = 0.6)

# Compare both versions
compare_wvar(wv.classical, wv.robust)

Now, let's try to estimate it with specific (e.g. user supplied) and guessed (e.g. program generated) parameters.

## Estimation Modes ##

# Use a specific initial starting value
o.specific = gmwm_imu(AR1(phi=.98,sigma2=.05) + WN(sigma2=.95), data = d)

# Let the program guess a good starting value
o.guess = gmwm_imu(AR1()+WN(), data = d)

To run inference or view the parameter estimates, we do:

## View Model Info ##

# Standard summary

# View with asymptotic inference
summary(o.specific, inference = T)

# View with bootstrapped inference
summary(o.specific, inference = T, bs.gof = T)

Alternatively, we can let the program try to figure out the best model for the data using the Wavelet Information Criteria (WIC):

## Model selection ##

# Separate Models - Compares 2*AR1() and AR1() + WN() under common model 2*AR1() + WN()
# Note: This function created a shared model (e.g. 2*AR1() + WN()) if not supplied to obtain the WIC. 
ms.sep = rank_models(AR1()+WN(), 2*AR1(), data = d, model.type="imu")

# Nested version - Compares AR1() + WN(), AR1(), WN()
ms.nested = rank_models(AR1()+WN(), data = d, nested = TRUE, model.type = "imu")

# Bootstrapped Optimism = rank_models(AR1()+WN(), WN(), data = d, bootstrap = TRUE, model.type = "imu")

# See automatic selection fit

# View model picked:

Last, but certainly not least, we can also approximate a contaminated sample with robust methodology:

## Data generation ##
# Specify model
model = AR1(phi = .99, sigma2 = .01) + WN(sigma2 = 1)

# Generate Data
N = 1e3
sim.ts = gen_gts(n, model)

# Contaminate Data
cont.eps = 0.01
cont.num = sample(1:N, round(N*cont.eps))
sim.ts[cont.num,] = sim.ts[cont.num,] + rnorm(round(N*cont.eps),0,sqrt(100))

# Plot the data

# Classical Wavelet Variance
wv.classic = wvar(sim.ts)

# Robust Wavelet Variance
wv.robust = wvar(sim.ts, robust = TRUE, eff = 0.6)

# Plot the Classical vs. Robust WV
compare_wvar(wv.classic, wv.robust, split = FALSE)

# Run robust estimation
o = gmwm_imu(model, sim.ts, robust = TRUE, eff = 0.6)

# Robust information

Install Instructions

To install the gmwm package, there are three options: CRAN (Stable), GitHub (Developmental), or SMAC (stable - offline).

Recommended R Interface

We firmly recommend that any users of this package use the RStudio IDE over the default R GUI.

Installing the package through CRAN (Stable)

The installation process with CRAN is the simplest


Installing the package this way gives you access to stable features. Furthermore, the installation itself does not require a compiler or preinstalling any dependencies. However, we are limited to updating the package on CRAN to once every month. Thus, there may be some lag between when features are developed and when they are available on this version.

Installing the package through GitHub (Developmental)

For users who are interested in having the latest and greatest developments withing wavelets or GMWM methodology, this option is ideal. Though, there is considerably more work that a user must do to have a stable version of the package. The setup to obtain the development version is platform dependent.

Specifically, one must have a compiler installed on your system that is compatible with R.

For help on obtaining a compiler consult:

Depending on your operating system, further requirements exist such as:


Some user report the need to use X11 to suppress shared library errors. To install X11, visit


Both curl and libxml are required.

For Debian systems, enter the following in terminal:

sudo apt-get install curl libcurl3 libcurl3-dev libxml2 libxml2-dev

For RHEL systems, enter the following in terminal:

sudo yum install curl curl-devel libxml2 libxml2-dev

All Systems

With the system dependency taken care of, we continue on by installing the R specific package dependencies and finally the package itself by doing the following in an R session:

# Install dependencies

# Install the package from GitHub without Vignettes/User Guides

# Install the package from GitHub with Vignettes/User Guides
# Note: This will be a longer install as the vignettes must be built.
devtools::install_github("SMAC-Group/gmwm", build_vignettes = TRUE)

Installing the package from (Stable - offline)

Lastly, we will be offering a source .tar that is able to be install offline - after being downloaded - on the website.

# Install the dependencies

# Local installation
install.packages("GMWM", repos = NULL, type="source")

Supplementary data package

To test the package performance on real-world data that is stationary or work with some of the examples, you will need to download and install the imudata and/or the datapkg R package.

To do so, please use the following installation method within the gmwm R package:

# Install the imudata package containing real world IMU data sets

# Install the datapkg package containing miscellaneous data sets

For more information about the imudata and datapkg package, see the and

User Guides

Various guides ship with package or are available on to provide insight into how to use the different methods. At the present time, the following vignettes are available:

  1. Process to Haar Wavelet Variance (Online)


The license this source code is released under is the GNU AFFERO GENERAL PUBLIC LICENSE (AGPL) v3.0. In some cases, the GPL license does apply. However, in the majority of the cases, the license in effect is the GNU AFFERO GENERAL PUBLIC LICENSE (AGPL) v3.0 as the computational code is heavily dependent on Armadilllo, which use the MPL license that enables us to recast our code to use the GNU AFFERO GENERAL PUBLIC LICENSE (AGPL) v3.0. See the LICENSE file for full text. Otherwise, please consult TLDR Legal or GNU which will provide a synopsis of the restrictions placed upon the code. Please note, this does NOT excuse you from talking about licensing with a lawyer!