Example: GARCH

The data for this example are generated to follow a GARCH(p,q) process by using a random number generation function sgarch . The data set is analyzed and estimates of sigma, the AR parameters, and the MA parameters are returned. The values of the Log-likelihood function and the Akaike Information Criterion are returned.

using System;
using Imsl.Stat;
using PrintMatrix = Imsl.Math.PrintMatrix;

public class GARCHEx1
{
    static private void  sgarch(int p, int q, int m, double[] x, 
        double[] y, double[] z, double[] y0, double[] sigma)
    {
        int i, j, l;
        double s1, s2, s3;
        Imsl.Stat.Random rand = new Imsl.Stat.Random(182198625);
        rand.Multiplier = 16807;

        for (i = 0; i < m + 1000; i++)
            z[i] = rand.NextNormal();
        
        l = System.Math.Max(p, q);
        l = System.Math.Max(l, 1);
        for (i = 0; i < l; i++)
            y0[i] = z[i] * x[0];
        
        /* COMPUTE THE INITIAL VALUE OF SIGMA */
        s3 = 0.0;
        if (System.Math.Max(p, q) >= 1)
        {
            for (i = 1; i < (p + q + 1); i++)
                s3 += x[i];
        }
        for (i = 0; i < l; i++)
            sigma[i] = x[0] / (1.0 - s3);
        for (i = l; i < (m + 1000); i++)
        {
            s1 = 0.0;
            s2 = 0.0;
            if (q >= 1)
            {
                for (j = 0; j < q; j++)
                    s1 += x[j + 1] * y0[i - j - 1] * y0[i - j - 1];
            }
            if (p >= 1)
            {
                for (j = 0; j < p; j++)
                    s2 += x[q + 1 + j] * sigma[i - j - 1];
            }
            sigma[i] = x[0] + s1 + s2;
            y0[i] = z[i] * Math.Sqrt(sigma[i]);
        }
        /*
         * DISCARD THE FIRST 1000 SIMULATED OBSERVATIONS
         */
        for (i = 0; i < m; i++)
            y[i] = y0[1000 + i];
        return ;
    }
    

    public static void  Main(String[] args)
    {
        int n, p, q, m;
        double[] x = new double[]{1.3, 0.2, 0.3, 0.4};
        double[] xguess = new double[]{1.0, 0.1, 0.2, 0.3};
        double[] y = new double[1000];
        double[] wk1 = new double[2000];
        double[] wk2 = new double[2000];
        double[] wk3 = new double[2000];

        m = 1000;
        p = 2;
        q = 1;
        n = p + q + 1;
        sgarch(p, q, m, x, y, wk1, wk2, wk3);
        
        GARCH garch = new GARCH(p, q, y, xguess);
        garch.Compute();
        
        Console.Out.WriteLine
            ("Sigma estimate is " + garch.Sigma.ToString("0.000"));
        Console.Out.WriteLine();
        new PrintMatrix("AR estimate is ").Print(garch.GetAR());
        new PrintMatrix("MR estimate is ").Print(garch.GetMA());
        Console.Out.WriteLine("Log-likelihood function value is " + 
            garch.LogLikelihood.ToString("0.000"));
        Console.Out.WriteLine("Akaike Information Criterion value is "
             + garch.Akaike.ToString("0.000"));
    }
}

Output

Sigma estimate is 1.692

   AR estimate is 
           0          
0  0.244996841351061  
1  0.337228450714669  

  MR estimate is 
          0         
0  0.3095927608719  

Log-likelihood function value is -2707.073
Akaike Information Criterion value is 5422.146