package com.imsl.test.example.stat;

import java.text.*;
import com.imsl.stat.*;
import com.imsl.math.*;
import com.imsl.*;

/**
 * <p>
 * Estimates missing values for a generated
 * \( \text{AR}(1) \) series. </p>
 * <p>
 * The data in this example was artificially generated using an autoregressive
 * time series with a lag of \(1\), i.e., an \(\text{AR}(1)\). The constant term
 * in the model was set to zero and \(-0.7\) was used for the autoregressive
 * coefficient. The data were generated from a random Gaussian distribution with
 * a mean of zero and an innovation variance of \(0.51\). This series is
 * stationary with \(\text{var}(Y) = 1.0\).
 * </p>
 * <p>
 * Two hundred values were generated. For this example, six values at times
 * \(t=\{130, 140, 141, 160, 175, 176\}\) are removed and designated as missing.
 * <code>ARMAEstimateMissing</code> is used to estimate these missing values
 * using each of its estimation methods. The missing value estimates are
 * compared to the actual values generated in the full series.</p>
 * <p>
 * As expected, the \(\text{AR}(1)\) method produces the best missing value
 * estimates in this example, closely followed by the \(\text{AR}(p)\)
 * method.</p>
 *
 * @see <a href="ARMAEstimateMissingEx1.java">Code</a>
 * @see <a href="doc-files/ARMAEstimateMissingEx1.out">Output</a>
 */
public class ARMAEstimateMissingEx1 {

    public static void main(String args[]) throws Exception {
        int i, j, k;
        int maxlag = 20, n_obs = 194, n_miss = 6;
        int[] missing_index, tpointsMiss, tpointsComplete;
        double missVar = 0;
        double sum = 0;
        double variance = 0;
        double[] y, yMiss;
        double[] yComplete = {
            1.30540, -1.37166, 1.47905, -0.91059, 1.36191, -2.16966, 3.11254,
            -1.99536, 2.29740, -1.82474, -0.25445, 0.33519, -0.25480, -0.50574,
            -0.21429, -0.45932, -0.63813, 0.25646, -0.46243, -0.44104, 0.42733,
            0.61102, -0.82417, 1.48537, -1.57733, -0.09846, 0.46311, 0.49156,
            -1.66090, 2.02808, -1.45768, 1.36115, -0.65973, 1.13332, -0.86285,
            1.23848, -0.57301, -0.28210, 0.20195, 0.06981, 0.28454, 0.19745,
            -0.16490, -1.05019, 0.78652, -0.40447, 0.71514, -0.90003, 1.83604,
            -2.51205, 1.00526, -1.01683, 1.70691, -1.86564, 1.84912, -1.33120,
            2.35105, -0.45579, -0.57773, -0.55226, 0.88371, 0.23138, 0.59984,
            0.31971, 0.59849, 0.41873, -0.46955, 0.53003, -1.17203, 1.52937,
            -0.48017, -0.93830, 1.00651, -1.41493, -0.42188, -0.67010, 0.58079,
            -0.96193, 0.22763, -0.92214, 1.35697, -1.47008, 2.47841, -1.50522,
            0.41650, -0.21669, -0.90297, 0.00274, -1.04863, 0.66192, -0.39143,
            0.40779, -0.68174, -0.04700, -0.84469, 0.30735, -0.68412, 0.25888,
            -1.08642, 0.52928, 0.72168, -0.18199, -0.09499, 0.67610, 0.14636,
            0.46846, -0.13989, 0.50856, -0.22268, 0.92756, 0.73069, 0.78998,
            -1.01650, 1.25637, -2.36179, 1.99616, -1.54326, 1.38220, 0.19674,
            -0.85241, 0.40463, 0.39523, -0.60721, 0.25041, -1.24967, 0.26727,
            1.40042, -0.66963, 1.26049, -0.92074, 0.05909, -0.61926, 1.41550,
            0.25537, -0.13240, -0.07543, 0.10413, 1.42445, -1.37379, 0.44382,
            -1.57210, 2.04702, -2.22450, 1.27698, 0.01073, -0.88459, 0.88194,
            -0.25019, 0.70224, -0.41855, 0.93850, 0.36007, -0.46043, 0.18645,
            0.06337, 0.29414, -0.20054, 0.83078, -1.62530, 2.64925, -1.25355,
            1.59094, -1.00684, 1.03196, -1.58045, 2.04295, -2.38264, 1.65095,
            -0.33273, -1.29092, 0.14020, -0.11434, 0.04392, 0.05293, -0.42277,
            0.59143, -0.03347, -0.58457, 0.87030, 0.19985, -0.73500, 0.73640,
            0.29531, 0.22325, -0.60035, 1.42253, -1.11278, 1.30468, -0.41923,
            -0.38019, 0.50937, 0.23051, 0.46496, 0.02459, -0.68478, 0.25821,
            1.17655, -2.26629, 1.41173, -0.68331
        };
        ARMAEstimateMissing estMiss;
        ARAutoUnivariate arAuto;
        String title = " ";
        String[] colLabels = {"TIME", "ACTUAL", "PREDICTED", "DIFFERENCE"};
        PrintMatrixFormat pmf = new PrintMatrixFormat();
        PrintMatrix pm = new PrintMatrix();
        NumberFormat nf = NumberFormat.getNumberInstance();
        nf.setMinimumFractionDigits(3);
        nf.setMaximumFractionDigits(3);
        pmf.setNumberFormat(nf);
        pmf.setColumnLabels(colLabels);
        pmf.setFirstRowNumber(1);
        pm.setColumnSpacing(3);

        /* setup missing data arrays */
        tpointsComplete = new int[200];
        tpointsMiss = new int[194];
        yMiss = new double[194];
        for (i = 1; i <= 200; i++) {
            tpointsComplete[i - 1] = i;
        }
        tpointsMiss[0] = tpointsComplete[0];
        yMiss[0] = yComplete[0];
        k = 0;
        for (i = 1; i < 200; i++) {
            /* Generate series with missing values */
            if (i != 129 && i != 139 && i != 140 && i != 159
                    && i != 174 && i != 175) {
                k += 1;
                tpointsMiss[k] = tpointsComplete[i];
                yMiss[k] = yComplete[i];
            }
        }
        n_obs = k + 1;

        for (j = 0; j <= 3; j++) {
            estMiss = new ARMAEstimateMissing(tpointsMiss, yMiss);
            switch (j) {
                case ARMAEstimateMissing.MEDIAN:
                    estMiss.setMissingValueMethod(ARMAEstimateMissing.MEDIAN);
                    title = "MEDIAN ESTIMATES";
                    break;
                case ARMAEstimateMissing.CUBIC_SPLINE:
                    estMiss.setMissingValueMethod(
                            ARMAEstimateMissing.CUBIC_SPLINE);
                    title = "CUBIC SPLINE ESTIMATES";
                    break;
                case ARMAEstimateMissing.AR_1:
                    estMiss.setMissingValueMethod(ARMAEstimateMissing.AR_1);
                    title = "AR(1) ESTIMATES";
                    break;
                case ARMAEstimateMissing.AR_P:
                    estMiss.setMaxlag(maxlag);
                    estMiss.setMissingValueMethod(ARMAEstimateMissing.AR_P);
                    estMiss.setEstimationMethod(
                            ARMAEstimateMissing.METHOD_OF_MOMENTS);
                    title = "AR(P) ESTIMATES";
                    break;
            }
            WarningObject currentWarningLevel = Warning.getWarning();
            /* For some data it is useful to turn off warnings produced by
             * the ARMA estimation process.  This is only necessary for
             * the AR_1 and AR_P estimation methods
             */
            Warning.setWarning(null);                // turn off warnings
            y = estMiss.getCompleteTimeSeries();
            Warning.setWarning(currentWarningLevel); // turn on warnings
            missing_index = estMiss.getMissingTimes();
            n_miss = y.length - yMiss.length;
            double[][] printOutput = new double[n_miss][4];
            sum = 0;
            for (i = 0; i < n_miss; i++) {
                k = missing_index[i];
                printOutput[i][0] = tpointsComplete[k];
                printOutput[i][1] = yComplete[k];
                printOutput[i][2] = y[k];
                printOutput[i][3] = Math.abs(yComplete[k] - y[k]);
                sum += Math.pow(printOutput[i][3], 2);
            }
            arAuto = new ARAutoUnivariate(maxlag, y);
            arAuto.compute();
            variance = arAuto.getInnovationVariance();
            pm.setTitle(title);
            pm.print(pmf, printOutput);
            missVar = sum / n_miss;
            System.out.println(
                    "Innovation Variance Analysis - Estimate (percent of actual)");
            System.out.println("         Missing Values(only): " + missVar
                    + " (" + Math.round(100.0 * missVar / 0.51) + "%)");
            System.out.println("         Entire  Series:       " + variance
                    + " (" + Math.round(100.0 * variance / 0.51) + "%)");
            System.out.println(
                    "***********************************************************");
            System.out.println("");
        }
    }
}