R/package-carfima.R

In kisungyou/carfima: Continuous-Time Fractionally Integrated ARMA Process for Irregularly Spaced Long-Memory Time Series Data

#' Continuous-Time Fractionally Integrated ARMA Process for Irregularly Spaced Long-Memory Time Series Data
#' 
#' The R package \pkg{carfima} provides 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(\eqn{p, H, q}) model for \eqn{p>q} is specified in Tsai and Chan (2005) and 
#' it involves \eqn{p+q+2} unknown model parameters, i.e., \eqn{p} AR parameters, \eqn{q} MA parameters, 
#' Hurst parameter \eqn{H}, and process uncertainty (standard deviation) \eqn{\sigma}; see also \code{\link{carfima}}. 
#' 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 \eqn{p>2}. The toolbox also contains a function to simulate discrete time series 
#' data from CARFIMA(\eqn{p, H, q}) process given the model parameters and observation times. 
#' 
#' @details 
#' \tabular{ll}{
#' Package: \tab carfima\cr
#' Type: \tab Package\cr
#' Version: \tab 2.0.0\cr
#' License: \tab GPL-2\cr
#' Main functions: \tab \code{\link{carfima}}, \code{\link{carfima.loglik}}, \code{\link{carfima.sim}}\cr
#' } 
#' 
#' @examples 
#' \donttest{
#' ##### Irregularly spaced observation time generation.
#' 
#' length.time <- 10
#' time.temp <- rexp(length.time, rate = 2)
#' time <- rep(NA, length.time + 1)
#' time[1] <- 0
#' for (i in 2 : (length.time + 1)) {
#'   time[i] <- time[i - 1] + time.temp[i - 1]
#'  }
#'  time <- time[-1]
#'  
#'  ##### Data genration for CARFIMA(1, H, 0) based on the observation times. 
#'
#'  parameter <- c(-0.4, 0.75, 0.2) 
#'  # AR parameter alpha = -0.4
#'  # Hurst parameter = 0.75
#'  # process uncertainty (standard deviation) sigma = 0.2
#'  y <- carfima.sim(parameter = parameter, time = time, ar.p = 1, ma.q = 0)  
#'  
#'  ##### Fitting the CARFIMA(1, H, 0) model on the simulated data for MLEs.
#'  
#'  res <- carfima(Y = y, time = time, method = "mle", ar.p = 1, ma.q = 0)
#'  
#'  # It takes a long time due to the differential evolution algorithm (global optimizer).
#'  # res$mle; res$se; res$AIC; res$fitted.values
#'  
#'  ##### Fitting the CARFIMA(1, H, 0) model on the simulated data for Bayesian inference.
#'  res <- carfima(Y = y, time = time, method = "bayes",
#'                 ar.p = 1, ma.q = 0, 
#'                 bayes.param.ini = parameter, 
#'                 bayes.param.scale = c(rep(0.2, length(parameter))), 
#'                 bayes.n.warm = 100, bayes.n.sample = 1000)
#'                 
#'  # It takes a long time because the likelihood evaluation is computationally heavy.
#'  # The last number of bayes.param.scale is to update sigma2 (not sigma) on a log scale.
#'  # hist(res$param[, 1]); res$accept; res$AIC; res$fitted.values
#'  
#'  ##### Computing the log likelihood of the CARFIMA(1, H, 0) model given the parameters.
#'  
#'  loglik <- carfima.loglik(Y = y, time = time, ar.p = 1, ma.q = 0,
#'                           parameter = parameter, fitted = FALSE)
#'}
#' @references 
#' \insertRef{tsai_note_2000}{carfima}
#' 
#' \insertRef{tsai_maximum_2005}{carfima}
#' 
#' 
#' @docType package
#' @name package-carfima
#' @import cubature
#' @import Rdpack
#' @import DEoptim
#' @import utils
#' @importFrom truncnorm rtruncnorm dtruncnorm
#' @importFrom invgamma dinvgamma
#' @importFrom numDeriv hessian
#' @importFrom MASS mvrnorm
#' @importFrom stats integrate dnorm median rexp rnorm
#' @importFrom Rcpp evalCpp
#' @useDynLib carfima, .registration=TRUE
NULL

##  .registration=TRUE