We provide a toolbox to fit a continuoustime fractionally integrated ARMA process (CARFIMA) on univariate and irregularly spaced time series data via frequentist or Bayesian machinery. A generalorder CARFIMA(p, H, q) model for p>q is specified in Tsai and Chan (2005) <doi:10.1111/j.14679868.2005.00522.x> 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.
Package details 


Author  Hyungsuk Tak [aut] (<https://orcid.org/0000000303348742>), Henghsiu Tsai [aut], Kisung You [aut, cre] (<https://orcid.org/000000028584459X>) 
Maintainer  Kisung You <[email protected]> 
License  GPL2 
Version  2.0.1 
Package repository  View on CRAN 
Installation 
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