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.