Public Release of GMWM v2.0.0

gmwm 2.0.0

This is the second general release of the Generalized Method of Wavelet Moments (GMWM) R Package. Considerable amount of work has been done to improve the user experience across all disciplines.

Highlights

• IMU Data Object Improvements
• New time series modeling term: GM (Gauss-Markov)
• More flexible MODWT, DWT, and AVAR Wrappers
• Improved IMU Parameter Search Algorithm
• Faster Batch WVAR Processing
• Rewritten visual model comparison
• Auto-version check on package load

Time Series Processed Model Syntax

• New model term that enables users to specify a guass-markov process (GM).
  • The GM is a reparameterization of an AR1 process using the freqeuncy of the data.
• Note: The conversion to and fro GM is done outside the C++ backend. Internally, the term is treated as an AR1 with frequency of 1.

Decomposition Methods

• New flexible R wrappers for
  • Discrete Wavelet Transform (DWT)
  • Maximal Overlap Discrete Wavelet Transform (MODWT)
  • Allan Variance (AVAR)
• Support is now available for taking up to a specific scale.
• DWT and MODWT now have built-in brick.wall support.
• New brick.wall R wrapper to later handle boundary coefficients.

Wavelet Variance

• Calculate the Wavelet Variance for DWT composition in addition to an MODWT decomposition.
• Change the level of decomposition for the WV.
• New batch data set processing function in C++

Model Comparison

• Reimplemented compare.models() function that removes the large spaces between plots.
• Labels are now around the top and right of the plot.

Data Objects

• imu and lts objects now have a frequency, unit, and name component.
• All data objects were rewritten so that data is placed first and foremost.
  • Attributes of the data are now accessed via attr(x,"name")
• Smart printing has been enabled for data objects. No longer will console be flooded with text!
  • Objects print the first and last 10 observations.
• update.* function
  • Added a means to update parameters of an object without recreating it.

IMU

• New grid search algorithm for IMU parameters that relies upon dominance of the first few scales.
• Improved loading experience with the addition of read.imu that returns an R IMU object type.
• The wvar.imu function now calls a new batch wrapper that processes multiple signals quickly.
• Added ability to subset IMU without losing attributes. (Limited to pairs of data.)

Package Load

• Auto-version check on package load
  • Connects to CRAN to see if a new package exists and alerts the user.
• More specific startup messages to help users access the resources of the package.

External Data Package Install

• Established the SMAC Group Data Repo
• Rewrote install_imudata to make use of the data repo
• Removed dl.file and install_ functions.

Internal

• Added quick create_imu() and create_wvar() objects to avoid long checks.
• Added ar1_to_gm() and gm_to_ar1() to convert to and for the GM object.
• Added is.*() functions for gmwm-based objects to avoid constantly calling inherit(x,"*").

Bug Fixes

• freq now affects the x-axis.
• The transformation with DR() is no longer the identity. Instead, we opt to use a logarithmic approach.
  • In transform_data, DR now has the absolute value taken and then a log.
  • In untransform_data, DR now is exponentiated.
• Capitalized axis when displaying imu graphs.

Known Bugs

• The compare.wvar does not work with type wvar.imu.

Initial Public Release of the GMWM R Package

gmwm 1.0.0

This is the first general release of the Generalized Method of Wavelet Moments (GMWM) R package. The package is meant to act as a platform for using the GMWM estimator.

Highlights

• High performing C++ routines to calculate wavelet variance, GMWM estimator, and more!
• Inference and Model Selection for the GMWM estimator,.
• Straightforward model specification of state-space model (or latent time series models) via natural inputs.
• Graphical features that enable the exploration of the Wavelet Variance and GMWM Estimation results.

Generalized Method of Wavelet Moments (GMWM)

• Efficient implementation of GMWM estimation techniques for ARMA and state-space models.
• Obtain results for time series with over two million observations in under 1.5 seconds!
• Effortlessly obtain initial starting values with a new grid search algorithm or use your own.
• Switch between different weighting matrices (e.g. approx,bootstrap,asymptotic)

Decomposition Methods

• The decomposition of process is available in three different C++ functions.
  • Discrete Wavelet Transform (DWT)
  • Maximal Overlap Discrete Wavelet Transform (MODWT)
  • Allan Variance (AVAR)
• Support for the following Daubechies wavelets:
  • d2 - Haar filter
• Extendable filter collection
  • Support a pull request to add a new filter!

Wavelet Variance

• Calculate the Wavelet Variance for a set of data underneath the Haar wavelet filter with either robust or classical techniques.
• Visualize the Wavelet Variance with plot(wvar(x))
• Compare the results of wavelet variances using compare.wvar()

Time Series Processed Model Syntax

• New model syntax that enables users to quickly specify models via ts.model S3 object.
• Specify models with initial starting parameters or let the built in grid search algorithm guess initial parameter values.
  • AR1() creates an AR1 modeling component with the program set to guess initial values.
  • AR1(phi = .3, sigma2 = 1) creates an AR1 modeling component with user supplied initial values.
• Support exists for:
  • Autoregressive order 1 (AR1(phi,sigma2))
  • Normal White Noise (WN(sigma2))
  • Random Walk (RW(sigma2))
  • Quantization Noise (QN(q2))
  • Moving Averages of order Q (MA(q))
  • Autoregressive of order P (AR(p))
  • Autoregressive - Moving Averages of orders P,Q (ARMA(p,q,sigma2))
• Chain different processes together through the use of the plus operator
  • E.g. mod = AR1() + WN() or `mod = AR1(phi = .9, sigma2 = 1) + WN(sigma2 = .1)
• Repeat processes through the use of the times operator
  • E.g. mod = 3*AR1()

Process Generation

• Computationally sound algorithms for generating:
  • Autoregressive - moving averages (ARMA)
  • Autoregressive processes of Order 1, P (AR1 or AR)
  • Moving Averages of Order Q (MA)
  • Normal White Noise (WN)
  • Random Walk (RW)
  • Quantization Noise (QN)
• Quick generation of latent processes via gen.gts(model, N)

Latent Time Series Demonstration

• See how different time series processes combine together via demo.lts().

Support

Primary support for this project was made possible by the Department of Statistics at the University of Illinois at Urbana-Champaign (UIUC). Furthermore, the contributions of undergraduate researcher Wenchao Yang for improving the visualization systems was supported, in part, by a grant from the Office of Undergraduate Research at UIUC. The project was mentored by James Balamuta and Prof. Stephane Guerrier.

Acknowledgement

We would like to thank the following individuals for their contributions and advice in the development of the GMWM methodology:

• Prof. Maria-Pia Victoria-Feser
• Dr. Jan Skaloud
• Dr. Yannick Stebler

Furthermore, we are also greatful to Dr. Jan Skaloud and Philipp Clausen of Geodetic Engineering Laboratory (TOPO), Swiss Federal Institute of Technology Lausanne (EPFL), topo.epfl.ch, Tel:+41(0)21 693 27 55 for providing data, which motivated the research and development of this package.