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 both frequentist and 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. Also, the model can account for heteroscedastic measurement errors, if the information about measurement error standard deviations is known. The package produces their maximum likelihood estimates and asymptotic uncertainties using a global optimizer called the differential evolution algorithm. It also produces posterior samples of the model parameters via Metropolis-Hastings within a Gibbs sampler equipped with adaptive Markov chain Monte Carlo. 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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2.0.2 by Hyungsuk Tak, 18 days ago

Browse source code at

Authors: Hyungsuk Tak , Henghsiu Tsai , and Kisung You

Documentation:   PDF Manual  

Task views:

GPL-2 license

Imports mvtnorm, DEoptim, pracma, truncnorm, invgamma

See at CRAN