Continuous-Time Fractionally Integrated ARMA Process for Irregularly Spaced Long-Memory Time Series Data

We provide a toolbox to fit a continuous-time fractionally integrated ARMA process (CARFIMA) on univariate and irregularly spaced time series data via frequentist or Bayesian machinery. A general-order CARFIMA(p, H, q) model for p>q is specified in Tsai and Chan (2005) and it involves (p+q+2) unknown model parameters, i.e., p AR parameters, q MA parameters, Hurst parameter H, and process uncertainty (standard deviation) sigma. The package produces their maximum likelihood estimates and asymptotic uncertainties using a global optimizer called the differential evolution algorithm. It also produces their posterior distributions via Metropolis within a Gibbs sampler equipped with adaptive Markov chain Monte Carlo for posterior sampling. These fitting procedures, however, may produce numerical errors if p>2. The toolbox also contains a function to simulate discrete time series data from CARFIMA(p, H, q) process given the model parameters and observation times.

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Code of Conduct

Please note that the 'carfima' project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.


News for carfima

Changes in version 2.0.1

  • Error fixed in likelihood evaluation (Mariusz Tarnopolski).
  • Initialize the following documentation:
    • NEWS for keeping record of updates.
    • README to briefly introduce the method.

Reference manual

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2.0.1 by Kisung You, a year ago

Browse source code at

Authors: Hyungsuk Tak [aut] , Henghsiu Tsai [aut] , Kisung You [aut, cre]

Documentation:   PDF Manual  

Task views:

GPL-2 license

Imports Rcpp, DEoptim, Rdpack, MASS, cubature, numDeriv, stats, utils, truncnorm, invgamma

Linking to Rcpp, RcppArmadillo, cubature

See at CRAN