package com.imsl.test.example.stat;

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

/**
 *
 * <p>
 * Fits an \(\text{ARMA}(2,1)\) to the Wolfer sunspot data and  
 * produces a forecast table. </p>
 *
 * 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. An \(\text{ARMA}(2,1)\) model is fitted to these data using the
 * Method of Moments. With <code>backward_origin=3</code>, the
 * <code>forecast</code> method is used to obtain forecasts starting from 1866,
 * 1867, 1868, and 1869, respectively. Note that the values in the first row of
 * the matrix returned by this method are the one-step ahead forecasts for 1867,
 * 1868, ..., 1870. The values in the second row are the two-step ahead
 * forecasts for 1868, 1869, ..., 1871, etc.</p>
 * <p>
 * Method <code>getForecast</code> is used to compute the one-step ahead
 * forecasts setting <code>backward_origin</code> = 10. This obtains the
 * one-step ahead forecasts for the last 10 observations in the series, i.e.
 * years 1860-1869, plus the next 5 years. The upper 90% confidence limits are
 * computed for these forecasts using the <code>getDeviations</code> method.
 * </p>
 *
 * @see <a href="ARMAEx3.java">Code</a>
 * @see <a href="doc-files/ARMAEx3.out">Output</a>
 */
public class ARMAEx3 {

    public static void main(String args[]) throws Exception {
        /* sunspots from 1770 to 1869 */
        double[] z = {
            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
        };
        int backwardOrigin = 3;
        double[][] printTable = new double[15][4];
        double[][] printEstimates = new double[1][4];
        double[] forecasts, deviations;
        PrintMatrixFormat pmf = new PrintMatrixFormat();
        PrintMatrix pm = new PrintMatrix();
        NumberFormat nf = NumberFormat.getNumberInstance();
        pm.setColumnSpacing(3);

        ARMA arma = new ARMA(2, 1, z);
        arma.compute();

        System.out.println("ARMA ESTIMATES");
        double[] ar = arma.getAR();
        double[] ma = arma.getMA();
        printEstimates[0][0] = arma.getConstant();
        printEstimates[0][1] = ar[0];
        printEstimates[0][2] = ar[1];
        printEstimates[0][3] = ma[0];
        String[] estimateLabels = {"Constant", "AR(1)", "AR(2)", "MA(1)"};
        pmf.setColumnLabels(estimateLabels);
        nf.setMinimumFractionDigits(5);
        nf.setMaximumFractionDigits(5);
        pmf.setNumberFormat(nf);
        pm.setTitle("ARMA ESTIMATES");
        pm.print(pmf, printEstimates);
        arma.setBackwardOrigin(backwardOrigin);

        String[] labels = {"From 1866", "From 1867",
            "From 1868", "From 1869"};
        pmf.setColumnLabels(labels);
        pmf.setFirstRowNumber(1);
        nf.setMinimumFractionDigits(1);
        nf.setMaximumFractionDigits(1);
        pmf.setNumberFormat(nf);
        pm.setTitle("FORECASTS");
        pm.print(pmf, arma.forecast(5));

        /* FORECASTING - An example of forecasting using the ARMA estimates
         * In this case, forecasts are returned for the last 10 values in the 
         * series followed by the forecasts for the next 5 values.
         */
        String[] forecastLabels = {
            "Observed", "Forecast", "Residual", "UCL(90%)"
        };
        pmf.setColumnLabels(forecastLabels);
        backwardOrigin = 10;
        arma.setBackwardOrigin(backwardOrigin);
        int n_forecast = 5;
        arma.setConfidence(0.9);
        forecasts = arma.getForecast(n_forecast);
        deviations = arma.getDeviations();
        for (int i = 0; i < backwardOrigin; i++) {
            printTable[i][0] = z[z.length - backwardOrigin + i];
            printTable[i][1] = forecasts[i];
            printTable[i][2] = z[z.length - backwardOrigin + i] - forecasts[i];
            printTable[i][3] = forecasts[i] + deviations[0];
        }
        for (int i = backwardOrigin; i < n_forecast + backwardOrigin; i++) {
            printTable[i][0] = Double.NaN;
            printTable[i][1] = forecasts[i];
            printTable[i][2] = Double.NaN;
            printTable[i][3] = forecasts[i] + deviations[i - backwardOrigin];
        }
        pmf.setFirstRowNumber(1869 - backwardOrigin + 1);
        pm.setTitle("ARMA ONE-STEP AHEAD FORECASTS");
        pm.print(pmf, printTable);
    }
}