public Dictionary <string, object> GetBestParameters(Dictionary <string, object> guess)
{
// Create a guess for the solver
var guessOmega = 1.0;
var guessAlpha = 0.2;
var guessBeta = 0.2;
if (guess != null)
{
guessOmega = (double)guess["Omega"];
guessAlpha = (double)guess["Alpha"];
guessBeta = (double)guess["Beta"];
}
// Constrain guess to admissible range
guessOmega = RestrictToOpenSet(guessOmega, 0.0, double.MaxValue);
guessAlpha = RestrictToOpenSet(guessAlpha, 0.0, 1.0);
guessBeta = RestrictToOpenSet(guessBeta, 0.0, 1.0 - guessAlpha);
var guessMucorr = guessAlpha + guessBeta;
var guessMuema = guessBeta / (guessAlpha + guessBeta);
// Transform guess to solver coordinates
var guessParameters = new double[3];
guessParameters[0] = Math.Log(guessOmega);
guessParameters[1] = -Math.Log(-Math.Log(guessMucorr));
guessParameters[2] = -Math.Log(-Math.Log(guessMuema));
var f = new GARCHMaxLikelihoodFunction(this);
var nm = new NelderMead(3);
nm.Function = solution => f.Value(solution);
nm.Convergence.MaximumEvaluations = _maxIterations;
nm.Maximize(guessParameters);
var bestParameters = nm.Solution;
// Transform parameters to GARCH parameters
var omega = Math.Exp(bestParameters[0]);
var mucorr = Math.Exp(-Math.Exp(-bestParameters[1]));
var muema = Math.Exp(-Math.Exp(-bestParameters[2]));
var beta = mucorr * muema;
var alpha = mucorr - beta;
double[] quantiles = { 0.01, 0.05, 0.5 };
var quantileValues = GetQuantilPredictionsForParameters(omega, alpha, beta, quantiles);
var results = new Dictionary <string, object>();
results.Add("Omega", omega);
results.Add("Alpha", alpha);
results.Add("Beta", beta);
results.Add("Szenarios", GetSzenarios(omega, alpha, beta));
//results.Add("Likelihood", GetLogLikelihoodForParameters(omega, alpha, beta));
results.Add("Vol", Math.Sqrt(GetLastResidualForParameters(omega, alpha, beta)));
results.Add("Quantile=1%", quantileValues[0]);
results.Add("Quantile=5%", quantileValues[1]);
results.Add("Quantile=50%", quantileValues[2]);
return(results);
}