package com.imsl.test.example.stat;

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

/**
 * <p>
 * Searches for the best fit seasonality for the Airline
 * data.</p>
 *
 * <p>
 * Consider the Airline Data (Box, Jenkins and Reinsel 1994, p. 547) consisting
 * of the monthly total number of international airline passengers from January
 * 1949 through December 1960. Class <code>ARSeasonalFit</code> is used to
 * compute the optimum seasonality representation of the adjusted series
 * $$W_t(s,d)=\Delta_{s_1}^{d_1}\Delta_{s_2}^{d_2}Z_t=
 * {(1-B^{s_1})}^{d_1}{(1-B^{s_2})}^{d_2}Z_t\rm{,}$$ where $$s=(1,1)$$ or
 * $$s=(1,12)$$ and $$d=(1,1)\rm{.}$$
 * </p>
 * <p>
 * As differenced series with minimum AIC,
 * $$W_t=\Delta_1^1\Delta_{12}^2Z_t=(Z_t-Z_{t-12})- (Z_{t-1}-Z_{t-13})\rm{,}$$
 * is identified.
 * </p>
 *
 * @see <a href="ARSeasonalFitEx1.java">Code</a>
 * @see <a href="doc-files/ARSeasonalFitEx1.out">Output</a>
 */

public class ARSeasonalFitEx1 {

    public static void main(String args[]) throws Exception {
        double[] z = {
            112, 118, 132, 129, 121, 135, 148, 148, 136, 119, 104, 118,
            115, 126, 141, 135, 125, 149, 170, 170, 158, 133, 114, 140,
            145, 150, 178, 163, 172, 178, 199, 199, 184, 162, 146, 166,
            171, 180, 193, 181, 183, 218, 230, 242, 209, 191, 172, 194,
            196, 196, 236, 235, 229, 243, 264, 272, 237, 211, 180, 201,
            204, 188, 235, 227, 234, 264, 302, 293, 259, 229, 203, 229,
            242, 233, 267, 269, 270, 315, 364, 347, 312, 274, 237, 278,
            284, 277, 317, 313, 318, 374, 413, 405, 355, 306, 271, 306,
            315, 301, 356, 348, 355, 422, 465, 467, 404, 347, 305, 336,
            340, 318, 362, 348, 363, 435, 491, 505, 404, 359, 310, 337,
            360, 342, 406, 396, 420, 472, 548, 559, 463, 407, 362, 405,
            417, 391, 419, 461, 472, 535, 622, 606, 508, 461, 390, 432
        };

        int sInit[][] = {{1, 1}, {1, 12}};

        ARSeasonalFit seasFit = new ARSeasonalFit(10, sInit, z);
        seasFit.compute();
        System.out.println("NLost = " + seasFit.getNLost());
        System.out.println("aic =" + seasFit.getAIC());
        new PrintMatrix("Best Periods (Optimum S)").
                print(seasFit.getOptimumS());
        new PrintMatrix("Best Orders (Optimum D)").
                print(seasFit.getOptimumD());
        System.out.println("Best AR order selected = " + seasFit.getAROrder());
        new PrintMatrix("AR Coefficients").print(seasFit.getAR());

        System.out.println("");
        double w[] = seasFit.getTransformedTimeSeries();
        double pack[][] = new double[30][2];
        for (int i = 0; i < 30; i++) {
            pack[i][0] = z[i];
            pack[i][1] = w[i];
        }
        PrintMatrix pm = new PrintMatrix();
        String str = "First 30 elements of the original time series "
                + "and differenced series";
        pm.setTitle(str);
        PrintMatrixFormat fmt = new PrintMatrixFormat();
        fmt.setColumnLabels(new String[]{"Original", "Differenced"});
        pm.print(fmt, pack);
    }
}