R/GASGamma_Estimate.R

In RasmusJensen96/VolatilityModelling: Work in progress volatility models for my personal usage

# Gamma-GAS filter
GASGAMMA_Filter <- function(vPar, vY) {
  ## Filtering the values of the filter
  ## Input: Parameters of the model (vPar) c(omega, alpha, beta, a)
  ##        Values to filter (vY)
  ## Output: filtered Mu_t
  ##         LLK with chosen parameters
  iT = length(vY)
  vMu = numeric(iT)
  vMuTilde = numeric(iT)

  dOmega = vPar[1]
  dAlpha = vPar[2]
  dBeta  = vPar[3]
  dA     = vPar[4]
  #initialize at the unconditional value
  vMuTilde[1] = dOmega/(1 - dBeta)
  vMu[1] = exp(vMuTilde[1])
  #The first loglikelihood value
  dLLK = Density_Gamma(vY[1], vMu[1], dA,cLog = TRUE)
  for(t in 2:iT) {
    vMuTilde[t] = dOmega + dBeta * vMuTilde[t - 1] + dAlpha * ( (dA / (vMuTilde[t-1] ^2))^(-1/2) * (dA*(vY[t-1]-vMu[t-1]))/(vMu[t-1])) # Updating the conditional mean (filtering)
    vMu[t] = exp(vMuTilde[t])
    dLLK = dLLK + Density_Gamma(vY[t], vMu[t], dA,cLog = TRUE) ## Calculating the total likelihood for selected model-parameters
  }
  lOut = list("dLLK" = dLLK,
              "vMu" = vMu)
  return(lOut)
}

Estimate_Gamma_GAS <- function(vY,Dates,iMaxIter) {
  require(DEoptim) # <- global optimizer
  ## Funcion "Estimate_Gamma_GAS":
  ## Input:   vY: Vector of observations, to which the Gamma-GAS model should be fitted
  ## Output:  vPar: estimated parameters
  #vPar: dOmega  = vPar[1]
  #dAlpha = vPar[2]
  #dBeta  = vPar[3]
  #dA     = vPar[4]
  ##         dLLK: Log Likelihood evaluated at the estimated (optimized) parameter values
  ##         ABIC: Average value of the Bayes Information Criterion, evaluated at optimum
  ##         FilteredMean: The filtered values of mu_t evaluated at optimum
  # maximize the likelihood using a global optimizer
  optimizer = DEoptim(Extract_LLH, lower = c(-0.5, 1e-3, 0.01, 0.1),
                      upper = c(0.5, 1.5, 0.999, 300), DEoptim.control(itermax=iMaxIter), vY = vY)
  vPar = optimizer$optim$bestmem
  dLLK = -optimizer$optim$bestval

  if (optimizer$optim$bestval != 1e5){
    cat(paste0("Optimizer converged: Gamma-GAS model fit complete: with LLH  ", dLLK))
  } else {
    cat(paste0("Optimizer not converged, try a different sample or series"))
  }
  # run the filter
  FilteredValues = GASGAMMA_Filter(vPar, vY)[["vMu"]]

  iT = length(vY)

  #compute the average BIC: having 4 paramaters
  ABIC = (log(iT) * 4 - 2 * dLLK)/iT

  lOut = list()
  class(lOut) <- "FitModel"

  lOut[["vPar"]] = vPar
  lOut[["dLLK"]] = dLLK
  lOut[["ABIC"]] = ABIC
  lOut[["Filtered"]] = FilteredValues
  lOut[["Observations"]] = vY
  lOut[["Dates"]] = Dates
  lOut[["Model"]] = "GAS"
  lOut[["Dist"]] = "Gamma"
  lOut[["Targetfilter"]] = "Conditional mean"
  return(lOut)
}