getCrossCovariance
and getCrossCorrelation
are used to compute the cross-covariances and cross-correlations between 
and Y and between 
and Y with lags from -maximum_lag
= -10 through lag maximum_lag
= 10.Consider the Wolfer Sunspot Data (Y ) (Box and Jenkins 1976, page 530) along with data on northern light activity (X1) and earthquake activity (X2) (Robinson 1967, page 204) to be a three-channel time series. Methods getCrossCovariance
and getCrossCorrelation
are used to compute the cross-covariances and cross-correlations between and Y and between and Y with lags from -maximum_lag
= -10 through lag maximum_lag
= 10.
import java.text.*;
import com.imsl.stat.*;
import com.imsl.math.PrintMatrix;
import com.imsl.math.Matrix;
public class MultiCrossCorrelationEx1 {
public static void main(String args[]) throws Exception {
int i;
double x[][] = {{ 155.0, 66.0},
{ 113.0, 62.0},
{ 3.0, 66.0},
{ 10.0, 197.0},
{ 0.0, 63.0},
{ 0.0, 0.0},
{ 12.0, 121.0},
{ 86.0, 0.0},
{ 102.0, 113.0},
{ 20.0, 27.0},
{ 98.0, 107.0},
{ 116.0, 50.0},
{ 87.0, 122.0},
{ 131.0, 127.0},
{ 168.0, 152.0},
{ 173.0, 216.0},
{ 238.0, 171.0},
{ 146.0, 70.0},
{ 0.0, 141.0},
{ 0.0, 69.0},
{ 0.0, 160.0},
{ 0.0, 92.0},
{ 12.0, 70.0},
{ 0.0, 46.0},
{ 37.0, 96.0},
{ 14.0, 78.0},
{ 11.0, 110.0},
{ 28.0, 79.0},
{ 19.0, 85.0},
{ 30.0, 113.0},
{ 11.0, 59.0},
{ 26.0, 86.0},
{ 0.0, 199.0},
{ 29.0, 53.0},
{ 47.0, 81.0},
{ 36.0, 81.0},
{ 35.0, 156.0},
{ 17.0, 27.0},
{ 0.0, 81.0},
{ 3.0, 107.0},
{ 6.0, 152.0},
{ 18.0, 99.0},
{ 15.0, 177.0},
{ 0.0, 48.0},
{ 3.0, 70.0},
{ 9.0, 158.0},
{ 64.0, 22.0},
{ 126.0, 43.0},
{ 38.0, 102.0},
{ 33.0, 111.0},
{ 71.0, 90.0},
{ 24.0, 86.0},
{ 20.0, 119.0},
{ 22.0, 82.0},
{ 13.0, 79.0},
{ 35.0, 111.0},
{ 84.0, 60.0},
{ 119.0, 118.0},
{ 86.0, 206.0},
{ 71.0, 122.0},
{ 115.0, 134.0},
{ 91.0, 131.0},
{ 43.0, 84.0},
{ 67.0, 100.0},
{ 60.0, 99.0},
{ 49.0, 99.0},
{ 100.0, 69.0},
{ 150.0, 67.0},
{ 178.0, 26.0},
{ 187.0, 106.0},
{ 76.0, 108.0},
{ 75.0, 155.0},
{ 100.0, 40.0},
{ 68.0, 75.0},
{ 93.0, 99.0},
{ 20.0, 86.0},
{ 51.0, 127.0},
{ 72.0, 201.0},
{ 118.0, 76.0},
{ 146.0, 64.0},
{ 101.0, 31.0},
{ 61.0, 138.0},
{ 87.0, 163.0},
{ 53.0, 98.0},
{ 69.0, 70.0},
{ 46.0, 155.0},
{ 47.0, 97.0},
{ 35.0, 82.0},
{ 74.0, 90.0},
{ 104.0, 122.0},
{ 97.0, 70.0},
{ 106.0, 96.0},
{ 113.0, 111.0},
{ 103.0, 42.0},
{ 68.0, 97.0},
{ 67.0, 91.0},
{ 82.0, 64.0},
{ 89.0, 81.0},
{ 102.0, 162.0},
{ 110.0, 137.0}};
double y[][] = {{ 101.0},
{ 82.0},
{ 66.0},
{ 35.0},
{ 31.0},
{ 7.0},
{ 20.0},
{ 92.0},
{ 154.0},
{ 126.0},
{ 85.0},
{ 68.0},
{ 38.0},
{ 23.0},
{ 10.0},
{ 24.0},
{ 83.0},
{ 132.0},
{ 131.0},
{ 118.0},
{ 90.0},
{ 67.0},
{ 60.0},
{ 47.0},
{ 41.0},
{ 21.0},
{ 16.0},
{ 6.0},
{ 4.0},
{ 7.0},
{ 14.0},
{ 34.0},
{ 45.0},
{ 43.0},
{ 48.0},
{ 42.0},
{ 28.0},
{ 10.0},
{ 8.0},
{ 2.0},
{ 0.0},
{ 1.0},
{ 5.0},
{ 12.0},
{ 14.0},
{ 35.0},
{ 46.0},
{ 41.0},
{ 30.0},
{ 24.0},
{ 16.0},
{ 7.0},
{ 4.0},
{ 2.0},
{ 8.0},
{ 17.0},
{ 36.0},
{ 50.0},
{ 62.0},
{ 67.0},
{ 71.0},
{ 48.0},
{ 28.0},
{ 8.0},
{ 13.0},
{ 57.0},
{ 122.0},
{ 138.0},
{ 103.0},
{ 86.0},
{ 63.0},
{ 37.0},
{ 24.0},
{ 11.0},
{ 15.0},
{ 40.0},
{ 62.0},
{ 98.0},
{ 124.0},
{ 96.0},
{ 66.0},
{ 64.0},
{ 54.0},
{ 39.0},
{ 21.0},
{ 7.0},
{ 4.0},
{ 23.0},
{ 55.0},
{ 94.0},
{ 96.0},
{ 77.0},
{ 59.0},
{ 44.0},
{ 47.0},
{ 30.0},
{ 16.0},
{ 7.0},
{ 37.0},
{ 74.0}};
MultiCrossCorrelation mcc = new MultiCrossCorrelation(x, y, 10);
new PrintMatrix("Mean of X : ").print(mcc.getMeanX());
new PrintMatrix("Variance of X : ").print(mcc.getVarianceX());
new PrintMatrix("Mean of Y : ").print(mcc.getMeanY());
new PrintMatrix("Variance of Y : ").print(mcc.getVarianceY());
double[][][] ccv = new double[21][2][1];
double[][][] cc = new double[21][2][1];
ccv = mcc.getCrossCovariance();
System.out.println("Multichannel cross-covariance between X and Y");
for (i=0; i<21; i++) {
System.out.println("Lag K = "+(i-10));
new PrintMatrix("CrossCovariances : ").print(ccv[i]);
}
cc = mcc.getCrossCorrelation();
System.out.println("Multichannel cross-correlation between X and Y");
for (i=0; i<21; i++) {
System.out.println("Lag K = "+(i-10));
new PrintMatrix("CrossCorrelations : ").print(cc[i]);
}
}
}
Mean of X :
0
0 63.43
1 97.97
Variance of X :
0
0 2,643.685
1 1,978.429
Mean of Y :
0
0 46.94
Variance of Y :
0
0 1,383.756
Multichannel cross-covariance between X and Y
Lag K = -10
CrossCovariances :
0
0 -20.512
1 70.713
Lag K = -9
CrossCovariances :
0
0 65.024
1 38.136
Lag K = -8
CrossCovariances :
0
0 216.637
1 135.578
Lag K = -7
CrossCovariances :
0
0 246.794
1 100.362
Lag K = -6
CrossCovariances :
0
0 142.128
1 44.968
Lag K = -5
CrossCovariances :
0
0 50.697
1 -11.809
Lag K = -4
CrossCovariances :
0
0 72.685
1 32.693
Lag K = -3
CrossCovariances :
0
0 217.854
1 -40.119
Lag K = -2
CrossCovariances :
0
0 355.821
1 -152.649
Lag K = -1
CrossCovariances :
0
0 579.653
1 -212.95
Lag K = 0
CrossCovariances :
0
0 821.626
1 -104.752
Lag K = 1
CrossCovariances :
0
0 810.131
1 55.16
Lag K = 2
CrossCovariances :
0
0 628.385
1 84.775
Lag K = 3
CrossCovariances :
0
0 438.272
1 75.963
Lag K = 4
CrossCovariances :
0
0 238.793
1 200.383
Lag K = 5
CrossCovariances :
0
0 143.621
1 282.986
Lag K = 6
CrossCovariances :
0
0 252.974
1 234.393
Lag K = 7
CrossCovariances :
0
0 479.468
1 223.034
Lag K = 8
CrossCovariances :
0
0 724.912
1 124.457
Lag K = 9
CrossCovariances :
0
0 924.971
1 -79.517
Lag K = 10
CrossCovariances :
0
0 922.759
1 -279.286
Multichannel cross-correlation between X and Y
Lag K = -10
CrossCorrelations :
0
0 -0.011
1 0.043
Lag K = -9
CrossCorrelations :
0
0 0.034
1 0.023
Lag K = -8
CrossCorrelations :
0
0 0.113
1 0.082
Lag K = -7
CrossCorrelations :
0
0 0.129
1 0.061
Lag K = -6
CrossCorrelations :
0
0 0.074
1 0.027
Lag K = -5
CrossCorrelations :
0
0 0.027
1 -0.007
Lag K = -4
CrossCorrelations :
0
0 0.038
1 0.02
Lag K = -3
CrossCorrelations :
0
0 0.114
1 -0.024
Lag K = -2
CrossCorrelations :
0
0 0.186
1 -0.092
Lag K = -1
CrossCorrelations :
0
0 0.303
1 -0.129
Lag K = 0
CrossCorrelations :
0
0 0.43
1 -0.063
Lag K = 1
CrossCorrelations :
0
0 0.424
1 0.033
Lag K = 2
CrossCorrelations :
0
0 0.329
1 0.051
Lag K = 3
CrossCorrelations :
0
0 0.229
1 0.046
Lag K = 4
CrossCorrelations :
0
0 0.125
1 0.121
Lag K = 5
CrossCorrelations :
0
0 0.075
1 0.171
Lag K = 6
CrossCorrelations :
0
0 0.132
1 0.142
Lag K = 7
CrossCorrelations :
0
0 0.251
1 0.135
Lag K = 8
CrossCorrelations :
0
0 0.379
1 0.075
Lag K = 9
CrossCorrelations :
0
0 0.484
1 -0.048
Lag K = 10
CrossCorrelations :
0
0 0.482
1 -0.169
Link to Java source.