package com.imsl.test.example.stat;

import com.imsl.stat.*;

/**
 * <p>
 * Performs a lack-of-fit test between an \(\text{ARMA}(2,1)\) and Wolfer's 
 * sunspot data.</p>
 * 
 * Consider the Wölfer Sunspot Data (Anderson 1971, page 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. An \(\text{ARMA}(2,1)\) with nonzero mean is fit to the series.
 * and the autocorrelations of the residuals are estimated
 * using the <code>AutoCorrelation</code> class. Class <code>LackOfFit</code> is
 * used to compute a portmanteau lack of fit test using 10 lags.
 *
 * The warning message from <code>ARMA</code> in the output can be ignored. (See
 * {@link ARMAEx2} for a full explanation of the warning message.)
 *
 * @see <a href="LackOfFitEx1.java">Code</a>
 * @see <a href="doc-files/LackOfFitEx1.out">Output</a>
 */

public class LackOfFitEx1 {

    public static void main(String args[]) throws Exception {
        int p = 2, q = 1, lagmax = 10, npfree = 4;
        double tolerance = 0.125;

        //  sunspot data for 1770 through 1869
        double[] x = {
            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
        };

        // Get residuals from ARMA(2,1) for autocorrelation/lack of fit
        ARMA arma = new ARMA(p, q, x);
        arma.setMethod(ARMA.LEAST_SQUARES);
        arma.setConvergenceTolerance(tolerance);
        arma.compute();
        double[] residuals = arma.getResidual();

        // Get autocorrelations from residuals for lack of fit test
        AutoCorrelation ac = new AutoCorrelation(residuals, lagmax);
        double[] correlations = ac.getAutoCorrelations();

        // Get lack of fit test statistic and p-value
        double[] result
                = LackOfFit.compute(x.length, correlations, npfree, lagmax);

        // Print parameter estimates, test statistic, and p-value
        // NOTE: Test Statistic Q follows a Chi-squared dist.
        System.out.println("Lack of Fit Statistic,  Q = " + result[0]);
        System.out.println("P-value of Q = " + result[1]);
    }
}