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.
using System;
using Imsl.Stat;
public class AutoARIMAEx3
{
public static void Main(String[] args)
{
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.CriticalValue = 3.8;
autoArima.Compute(3, 2, 1, 0);
autoArima.Forecast(6);
nOutliers = autoArima.NumberOfOutliers;
aic = autoArima.AIC;
optimumModel = autoArima.GetOptimumModelOrder();
outlierStatistics = autoArima.GetOutlierStatistics();
RSE = autoArima.ResidualStandardError;
outlierForecast = autoArima.GetForecast();
psiWeights = autoArima.GetPsiWeights();
probabilityLimits = autoArima.GetDeviations();
constant = autoArima.Constant;
ar = autoArima.GetAR();
ma = autoArima.GetMA();
Console.Out.WriteLine("\nMethod 3: Specified ARIMA model");
Console.Out.WriteLine();
Console.Out.WriteLine(
"Optimum Model: p={0,1:d}, q={1,1:d}, s={2,1:d}, d={3,1:d}",
optimumModel[0], optimumModel[1], optimumModel[2], optimumModel[3]);
Console.Out.WriteLine("\nNumber of outliers:{0,2:d}\n", nOutliers);
Console.Out.WriteLine("Outlier statistics:");
Console.Out.WriteLine(" Time Type");
for (int i = 0; i < nOutliers; i++)
Console.Out.WriteLine("{0,5:d}{1,8:d}", outlierStatistics[i, 0],
outlierStatistics[i, 1]);
Console.Out.WriteLine("\nAIC:{0,13:f6}", aic);
Console.Out.WriteLine("RSE:{0,13:f6}", RSE);
Console.Out.WriteLine();
Console.Out.WriteLine(" Parameters");
Console.Out.WriteLine(" constant:{0,11:f6}", constant);
for (int i = 0; i < ar.Length; i++)
Console.Out.WriteLine(" ar[{0,2:d}]:{1,13:f6}", i, ar[i]);
for (int i = 0; i < ma.Length; i++)
Console.Out.WriteLine(" ma[{0,2:d}]:{1,13:f6}", i, ma[i]);
Console.Out.WriteLine("\n\n * * * Forecast Table * * *");
Console.Out.WriteLine(" Exact forecast limits psi");
for (int i = 0; i < outlierForecast.Length; i++)
Console.Out.WriteLine("{0,7:f4}{1,11:f4}{2,11:f4}{3,11:f4}",
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 C# source.