This example is the same as example 2 but now method 3 with the optimum model parameters p = 3, q = 2, s = 1, d = 0
from Example 2 is chosen for outlier detection and forecasting.
import java.util.*;
import com.imsl.stat.*;
public class AutoARIMAEx3 {
public static void main(String args[]) throws Exception {
int nOutliers;
double aic, RSE, constant;
int[] optimumModel;
int[][] outlierStatistics;
double[] outlierForecast, ar, ma;
double[] psiWeights, probabilityLimits;
double[] x = {
12.8, 12.2, 11.9, 10.9, 10.6, 11.3, 11.1, 10.4, 10.0, 9.7, 9.7, 9.7,
11.1, 10.5, 10.3, 9.8, 9.8, 10.4, 10.4, 10.0, 9.7, 9.3, 9.6, 9.7,
10.8, 10.7, 10.3, 9.7, 9.5, 10.0, 10.0, 9.3, 9.0, 8.8, 8.9, 9.2,
10.4, 10.0, 9.6, 9.0, 8.5, 9.2, 9.0, 8.6, 8.3, 7.9, 8.0, 8.2,
9.3, 8.9, 8.9, 7.7, 7.6, 8.4, 8.5, 7.8, 7.6, 7.3, 7.2, 7.3,
8.5, 8.2, 7.9, 7.4, 7.1, 7.9, 7.7, 7.2, 7.0, 6.7, 6.8, 6.9,
7.8, 7.6, 7.4, 6.6, 6.8, 7.2, 7.2, 7.0, 6.6, 6.3, 6.8, 6.7,
8.1, 7.9, 7.6, 7.1, 7.2, 8.2, 8.1, 8.1, 8.2, 8.7, 9.0, 9.3,
10.5, 10.1, 9.9, 9.4, 9.2, 9.8, 9.9, 9.5, 9.0, 9.0, 9.4, 9.6,
11.0, 10.8, 10.4, 9.8, 9.7, 10.6, 10.5, 10.0, 9.8, 9.5, 9.7, 9.6,
10.9, 10.3, 10.4, 9.3, 9.3, 9.8, 9.8, 9.3, 8.9, 9.1, 9.1, 9.1,
10.2, 9.9, 9.4
};
double[] exactForecast = {8.7, 8.6, 9.3, 9.1, 8.8, 8.5};
int[] times = {
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48,
49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,
73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84,
85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96,
97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,
109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120,
121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135
};
AutoARIMA autoArima = new AutoARIMA(times, x);
autoArima.setCriticalValue(3.8);
autoArima.compute(3, 2, 1, 0);
autoArima.forecast(6);
nOutliers = autoArima.getNumberOfOutliers();
aic = autoArima.getAIC();
optimumModel = autoArima.getOptimumModelOrder();
outlierStatistics = autoArima.getOutlierStatistics();
RSE = autoArima.getResidualStandardError();
outlierForecast = autoArima.getForecast();
psiWeights = autoArima.getPsiWeights();
probabilityLimits = autoArima.getDeviations();
constant = autoArima.getConstant();
ar = autoArima.getAR();
ma = autoArima.getMA();
System.out.printf("%nMethod 3: Specified ARIMA model%n");
System.out.printf("%nOptimum Model: p=%d, q=%d, s=%d, d=%d%n",
optimumModel[0], optimumModel[1],
optimumModel[2], optimumModel[3]);
System.out.printf("%nNumber of outliers:%3d%n%n", nOutliers);
System.out.printf("Outlier statistics:%n");
System.out.printf(" Time%4sType%n", " ");
for (int i = 0; i < nOutliers; i++) {
System.out.printf("%5d%8d%n", outlierStatistics[i][0],
outlierStatistics[i][1]);
}
System.out.printf(Locale.ENGLISH, "%nAIC:%12.6f%n", aic);
System.out.printf(Locale.ENGLISH, "RSE%13.6f%n%n", RSE);
System.out.printf("%5sParameters%n", " ");
System.out.printf(Locale.ENGLISH, " constant:%10.6f%n", constant);
for (int i = 0; i < ar.length; i++) {
System.out.printf(Locale.ENGLISH, " ar[%d]:%13.6f%n", i, ar[i]);
}
for (int i = 0; i < ma.length; i++) {
System.out.printf(Locale.ENGLISH, " ma[%d]:%13.6f%n", i, ma[i]);
}
System.out.printf("%n%n%6s* * * Forecast Table * * *%n", " ");
System.out.printf("%2sExact%3sforecast%5slimits%8spsi%n",
" ", " ", " ", " ");
for (int i = 0; i < outlierForecast.length; i++) {
System.out.printf(Locale.ENGLISH, "%7.4f%11.4f%11.4f%11.4f%n",
exactForecast[i], outlierForecast[i],
probabilityLimits[i], psiWeights[i]);
}
}
}
Method 3: Specified ARIMA model
Optimum Model: p=3, q=2, s=1, d=0
Number of outliers: 1
Outlier statistics:
Time Type
109 0
AIC: 408.108176
RSE 0.412456
Parameters
constant: 0.554459
ar[0]: 1.940615
ar[1]: -1.898025
ar[2]: 0.897791
ma[0]: 1.115803
ma[1]: -0.911902
* * * Forecast Table * * *
Exact forecast limits psi
8.7000 9.1085 0.8084 0.8248
8.6000 9.1715 1.0479 0.6145
9.3000 9.5039 1.1597 0.5248
9.1000 9.7677 1.2349 0.5926
8.8000 9.7051 1.3245 0.7056
8.5000 9.3817 1.4421 0.7157
Link to Java source.