R/Ngarch.R

In KevinKotze/tsm: Time Series Modelling

#' Estimation of a non-symmertic GARCH that takes the form NGARCH(1,1) with normal innovations.
#'
#' @param rtn Time series variable.
#' @return non-symmertic GARCH results.
#' @examples


"Ngarch" <- function(rtn) {
  # The likelihood function "glkn" can be modified to fit more general NGARCH
  #  models.
  write(rtn, file = 'tmp.txt', ncol = 1)
  # obtain initial estimates
  mu = mean(rtn)
  par = c(mu, 0.01, 0.8, 0.01, 0.7)
  #
  #
  mm = optim(par, glkn, method = "Nelder-Mead", hessian = T)
  low = c(-10, 0, 0, 0, 0)
  upp = c(10, 1, 1, 0.4, 2)
  #mm=optim(par,glkn,method="L-BFGS-B",hessian=T,lower=low,upper=upp)
  ## Print the results
  par = mm$par
  H = mm$hessian
  Hi = solve(H)
  cat(" ", "\n")
  cat("Estimation results of NGARCH(1,1) model:", "\n")
  cat("estimates: ", par, "\n")
  se = sqrt(diag(Hi))
  cat("std.errors: ", se, "\n")
  tra = par / se
  cat("t-ratio: ", tra, "\n")
  # compute the volatility series and residuals
  ht = var(rtn)
  T = length(rtn)
  if (T > 40)
    ht = var(rtn[1:40])
  at = rtn - par[1]
  for (i in 2:T) {
    sig2t = par[2] + par[3] * ht[i - 1] + par[4] * (at[i - 1] - par[5] * sqrt(ht[i -
                                                                                   1])) ^ 2
    ht = c(ht, sig2t)
  }
  sigma.t = sqrt(ht)
  Ngarch <- list(residuals = at, volatility = sigma.t)
}

glkn <- function(par) {
  rtn = read.table("tmp.txt")[, 1]
  glkn = 0
  ht = var(rtn)
  T = length(rtn)
  if (T > 40)
    ht = var(rtn[1:40])
  at = rtn[1] - par[1]
  for (i in 2:T) {
    ept = rtn[i] - par[1]
    at = c(at, ept)
    sig2t = par[2] + par[3] * ht[i - 1] + par[4] * ht[i - 1] * (at[i - 1] /
                                                                  sqrt(ht[i - 1]) - par[5]) ^ 2
    ht = c(ht, sig2t)
    glkn = glkn + 0.5 * (log(sig2t) + ept ^ 2 / sig2t)
  }
  glkn
}