R/MethodOfCumulants_MTS.R

In TempStable: A Collection of Methods to Estimate Parameters of Different Tempered Stable Distributions

#' @importFrom moments all.moments
CumFinder_MTS <- function(x, jmax = 5) {
    raw.moments <- moments::all.moments(x, order.max = jmax)
    cumfrommom(raw.moments)[-1]
}

# Function origin is kim09. See charMTS().
MoCObjective_MTS <- function(x, parms) {

  c(F1 = x[5] + 2^(1-(x[1]+3)/2)*factorial((1-1)/2)*x[2]*gamma((1-x[1])/2)*
      (x[3]^(x[1]-1) - x[4]^(x[1]-1)) - parms[1],
    F2 = 2^(-(x[1]+3)/2)*sqrt(pi)*factorial(2)/factorial(2/2)*x[2]*
      gamma(2-x[1]/2)*(x[3]^(x[1]-2) - x[4]^(x[1]-2)) - parms[2],
    F3 = 2^(3-(x[1]+3)/2)*factorial((3-1)/2)*x[2]*gamma((3-x[1])/2)*
      (x[3]^(x[1]-3) - x[4]^(x[1]-3)) - parms[3],
    F4 = 2^(-(x[1]+3)/2)*sqrt(pi)*factorial(4)/factorial(4/2)*x[2]*
      gamma(4-x[1]/2)*(x[3]^(x[1]-4) - x[4]^(x[1]-4)) - parms[4],
    F5 = 2^(5-(x[1]+3)/2)*factorial((5-1)/2)*x[2]*gamma((5-x[1])/2)*
      (x[3]^(x[1]-5) - x[4]^(x[1]-5)) - parms[5]
  )
}

# Function origin is kim09. See charMTS().
#' @importFrom rootSolve multiroot
MoC_MTS <- function(x, theta0 = c(0.6, 1, 1, 1, 0), eps = 1e-06) {
    cumulants <- CumFinder_MTS(x)
    utils::capture.output(parroot <-
        rootSolve::multiroot(MoCObjective_MTS, theta0, parms = cumulants))
    theta <- parroot$root

    if (theta[1] > 1) {
        theta <- theta0
    }
    return(theta)
}