Computation of the GMAIC

This example shows how the empirical distribution of the GMAIC as defined in [1] can be computed by means of the library.

C#:

References:

NbbTs.dll

NbbEco.dll

NbbGeneralizedAirline.dll

Code:

using Nbb.TimeSeries.SimpleTS;
using Nbb.GeneralAirline;
using Nbb.SArima;

// Number of simulations
int nruns = 10000;

// Length of the series
int n = 150;

// MA polynomial:(1+q*B)(1+bq*B^12). Building of the Airline model.
double q = -0.5, bq = -.5;
SArimaModel arima = new SArimaModelBuilder().CreateAirlineModel(12, q, bq);

double[] gmaic = new double[nruns];

GeneralizedAirlineMonitor monitor = new GeneralizedAirlineMonitor();
for (int i = 0; i < nruns; ++i)
{
    double[] d = new ArimaModelBuilder().Generate(arima, n);
    TS ts = new TS(TSFrequency.Monthly, 1980, 0, d);
    monitor.Process(ts);

    Nbb.GeneralAirline.LLGeneralizedAirline[] ll = monitor.Results;
    // AIC for the airline model
    double aic0 = ll[0].Likelihood.AIC(2);

    // max AIC of the 5-1(3) models
    double aic1 = Double.MaxValue;
    int jmax = 1;
    for (int j = 1; j < ll.Length; ++j)
        if (ll[j].Model != null)
        {
            double curaic = ll[j].Likelihood.AIC(3);
            if (curaic < aic1)
            {
                aic1 = curaic;
                jmax = j;
            }
        }

    gmaic[i] = aic0 - aic1;
}

The code yields the following empirical distribution:

Distribution

PValue

Bibliography

[1] John A. D. Aston, David F. Findley, Kellie C. Wills, and Donald E. K. Martin (2004), "Generalizations of the Box-Jenkins Airline Model with Frequency-Specific Seasonal Coefficients and a Generalizaton of Akaike’s MAIC", presented at 2004 NBER/NSF Time Series Conference.