Consider the Wolfer Sunspot Data (Anderson 1971, p. 660) consisting of the number of sunspots observed each year from 1749 through 1924. The data set for this example consists of the number of sunspots observed from 1770 through 1869. This example computes the estimated autocovariances, estimated autocorrelations, and estimated standard errors of the autocorrelations using both Barlett and Moran formulas.
using System; using Imsl.Stat; using PrintMatrix = Imsl.Math.PrintMatrix; public class AutoCorrelationEx1 { public static void Main(String[] args) { double[] x = new double[]{ 100.8, 81.6, 66.5, 34.8, 30.6, 7, 19.8, 92.5, 154.4, 125.9, 84.8, 68.1, 38.5, 22.8, 10.2, 24.1, 82.9, 132, 130.9, 118.1, 89.9, 66.6, 60, 46.9, 41, 21.3, 16, 6.4, 4.1, 6.8, 14.5, 34, 45, 43.1, 47.5, 42.2, 28.1, 10.1, 8.1, 2.5, 0, 1.4, 5, 12.2, 13.9, 35.4, 45.8, 41.1, 30.4, 23.9, 15.7, 6.6, 4, 1.8, 8.5, 16.6, 36.3, 49.7, 62.5, 67, 71, 47.8, 27.5, 8.5, 13.2, 56.9, 121.5, 138.3, 103.2, 85.8, 63.2, 36.8, 24.2, 10.7, 15, 40.1, 61.5, 98.5, 124.3, 95.9, 66.5, 64.5, 54.2, 39, 20.6, 6.7, 4.3, 22.8, 54.8, 93.8, 95.7, 77.2, 59.1, 44, 47, 30.5, 16.3, 7.3, 37.3, 73.9}; AutoCorrelation ac = new AutoCorrelation(x, 20); new PrintMatrix ("AutoCovariances are: ").Print(ac.GetAutoCovariances()); Console.Out.WriteLine(); new PrintMatrix ("AutoCorrelations are: ").Print(ac.GetAutoCorrelations()); Console.Out.WriteLine("Mean = " + ac.Mean); Console.Out.WriteLine(); new PrintMatrix ("Standard Error using Bartlett are: ").Print (ac.GetStandardErrors(AutoCorrelation.StdErr.Bartletts)); Console.Out.WriteLine(); new PrintMatrix ("Standard Error using Moran are: ").Print (ac.GetStandardErrors(AutoCorrelation.StdErr.Morans)); Console.Out.WriteLine(); new PrintMatrix ("Partial AutoCovariances: "). Print(ac.GetPartialAutoCorrelations()); ac.Mean = 50; new PrintMatrix ("AutoCovariances are: ").Print (ac.GetAutoCovariances()); Console.Out.WriteLine(); new PrintMatrix ("AutoCorrelations are: "). Print(ac.GetAutoCorrelations()); Console.Out.WriteLine(); new PrintMatrix ("Standard Error using Bartlett are: ").Print (ac.GetStandardErrors(AutoCorrelation.StdErr.Bartletts)); } }
AutoCovariances are: 0 0 1382.908024 1 1115.02915024 2 592.00446848 3 95.29741072 4 -235.95179904 5 -370.0108088 6 -294.25541456 7 -60.44237232 8 227.63259792 9 458.38076816 10 567.8407384 11 546.12202864 12 398.93728688 13 197.75742912 14 26.89107936 15 -77.2807224 16 -143.73279616 17 -202.04799792 18 -245.37223168 19 -230.81567344 20 -142.8788232 AutoCorrelations are: 0 0 1 1 0.806293065691258 2 0.428086653780237 3 0.0689108813212006 4 -0.170620023128885 5 -0.267559955093586 6 -0.212780177317129 7 -0.043706718936501 8 0.164604293249802 9 0.331461500117813 10 0.410613524938228 11 0.394908424249623 12 0.288477093166393 13 0.143001143740562 14 0.0194453129877855 15 -0.0558827637549379 16 -0.10393518127421 17 -0.146103713633525 18 -0.17743206881559 19 -0.166906019369514 20 -0.103317661565611 Mean = 46.976 Standard Error using Bartlett are: 0 0 0.0347838253702384 1 0.0962419914340011 2 0.156783378574532 3 0.205766777086907 4 0.230955675779118 5 0.228994712235613 6 0.208621905639667 7 0.178475936561125 8 0.145727084432033 9 0.134405581638002 10 0.150675803916788 11 0.174348147103935 12 0.190619474429408 13 0.195490061669564 14 0.195892530944597 15 0.196285328179458 16 0.196020624500033 17 0.198716030900604 18 0.205358590947539 19 0.2093868822353 Standard Error using Moran are: 0 0 0.0985184366143778 1 0.0980196058819607 2 0.0975182235357506 3 0.0970142500145332 4 0.0965076447241154 5 0.0959983659991659 6 0.0954863710632231 7 0.0949716159867634 8 0.094454055643212 9 0.0939336436627724 10 0.0934103323839415 11 0.0928840728025648 12 0.0923548145182799 13 0.0918225056781811 14 0.0912870929175277 15 0.090748521297303 16 0.0902067342384192 17 0.0896616734523426 18 0.0891132788679007 19 0.0885614885540095 Partial AutoCovariances: 0 0 0.806293065691258 1 -0.634544877310468 2 0.0782508772709519 3 -0.0585660846582815 4 -0.00094221571933657 5 0.171719898229681 6 0.108591873581717 7 0.11000138764865 8 0.0785374339029981 9 0.0791563332964613 10 0.0687065876031485 11 -0.0378019674610775 12 0.0811184838397538 13 0.0334124214991749 14 -0.0348467839607946 15 -0.130648157884444 16 -0.154900984829049 17 -0.119085063160732 18 -0.0161889037437313 19 -0.00385175459253345 AutoCovariances are: 0 0 1392.0526 1 1126.5241 2 604.1624 3 106.7545 4 -225.882 5 -361.0259 6 -286.5701 7 -53.7603 8 235.9665 9 470.7857 10 584.0143 11 564.7639 12 418.3631 13 216.1044 14 43.125 15 -63.4683 16 -131.5012 17 -189.0627 18 -229.6888 19 -212.1559 20 -121.5693 AutoCorrelations are: 0 0 1 1 0.809253975029392 2 0.434008312616923 3 0.0766885532917362 4 -0.162265420142888 5 -0.259347886710603 6 -0.205861545749061 7 -0.0386194458456527 8 0.16950975846746 9 0.338195338308337 10 0.419534649768263 11 0.405705861976767 12 0.300536847530043 13 0.155241547625427 14 0.0309794328174093 15 -0.04559332025241 16 -0.0944656832651295 17 -0.135815773053403 18 -0.165000086922003 19 -0.152405088715757 20 -0.0873309672350025 Standard Error using Bartlett are: 0 0 0.0344591054641365 1 0.0972222809088609 2 0.15947410033087 3 0.209799660647689 4 0.235599778243579 5 0.233236443705991 6 0.211657508693781 7 0.180412936841618 8 0.14689653606348 9 0.133747601649498 10 0.148150190923942 11 0.172282351100035 12 0.190275929042947 13 0.196791614240352 14 0.197983743593071 15 0.198474748794747 16 0.198318159677368 17 0.201022833791806 18 0.207071652966429 19 0.210217650328868Link to C# source.