Rational Linear Dynamic Models (RLDM)

This RLDM (Rational Linear Dynamic Models) R package provides models for stationary processes with a rational spectral density and methods for their estimation. We will refer to them as rational models. It builds heavily on its sister R package rationalmatrices, see https://bfunovits.github.io/rationalmatrices/.

Installation

You can install the latest version of the code using the remotes R package.

remotes::install_github("bfunovits/RLDM")

Content

The package provides the following sets of functions whose documentation can be found in the reference page https://bfunovits.github.io/RLDM/reference of the website https://bfunovits.github.io/RLDM/ (created with https://pkgdown.r-lib.org/):

• Classes for the construction of rational models (consisting of an input covariance matrix and a rational matrix function from the rationalmatrices package):
  • VARMA models armamod()
  • State space models stspmod()
  • Right matrix fraction description (RMFD) models rmfdmod() (which is experimental)
• Templates for filling the linear parameters with deep parameters through an affine mapping. Consists of
  • a matrix $H$ where the number of rows is the number of linear parameters in a given model and the number of columns is the number of deep parameters in a given model
  • a column vector $h$ of appropriate dimension

See help("model structures") and help("local model structures") for more details.

• Generic functions to create objects which are derived from these rational models

  • The autocovariance sequence, see autocov()
  • Spectral density, see spectrald()
  • The transfer function/impulse response function (IRF), see impresp()
    • Forecast error variance decomposition, see fevardec(), for a given IRF
  • Frequency response (the transfer function evaluated on the unit circle), see freqresp()

• Several other generic functions which extend R’s generic functions

  • plot(), print(), str(), predict()

• Some helpers for estimation methods: solve_de(), solve_inverse_de(), and more

• Moment estimation methods for

  • AR models, see e.g. est_ar()
  • ARMA models, see the Hannan-Rissannen-Kavalieris algorithm in est_arma_hrk3()
  • state space models, see e.g. est_stsp_cca()

• Likelihood estimation methods

  • ll()
  • ll_theta() and ll_FUN() for the estimation of the deep parameters of a rational model
  • ll_kf()

• Some more tooling like

  • simulation in sim()
  • model comparison in KL_divergence(), pm_test(), compare_estimates()

Getting Started

RLDM includes comprehensive documentation organized by user level:

1. New to RLDM? Start with vignette("0_getting_started")
   • Practical introduction with simple examples
   • AR models and multivariate VAR/VARMA systems
   • ~10-15 minute read with executable code
2. Want a complete workflow example? See vignette("1_case_study")
   • Blanchard-Quah economic data analysis
   • Comparing AR, state space, and ARMA models
   • Model selection, diagnostics, and forecasting
3. Need technical details? Consult vignette("2_technical_reference")
   • Complete class and method documentation
   • Mathematical foundations
   • Method selection guidance

Installation Notes

The package depends on rationalmatrices. Install both:

remotes::install_github("bfunovits/rationalmatrices")
remotes::install_github("bfunovits/RLDM")

Vignette Building: To build vignettes locally, you need pandoc-citeproc installed on your system: - Ubuntu/Debian: sudo apt-get install pandoc-citeproc - macOS: brew install pandoc-citeproc - Windows: Included in pandoc installer

Pre-built vignettes are available on the package website.

Then load and explore:

library(RLDM)
browseVignettes("RLDM")  # View all vignettes (if built locally)
vignette("0_getting_started")  # Access specific vignette