package com.imsl.test.example.stat;

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

/**
 * <p>
 * Finds the minimum AIC autoregressive model for the Wolfer sunspot data.</p>
 * <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. In this example,
 * <a href="../../../stat/ARAutoUnivariate.html">ARAutoUnivariate</a>
 * found the minimum AIC fit is an autoregressive model with 3 lags:
 * $$\tilde{W_t}=\phi_1\tilde{W_{t-1}}+\phi_2
 * \tilde{W_{t-2}}+\phi_3\tilde{W_{t-3}} + a_t\rm{,}$$ where $$\tilde{W_t} :=
 * W_t - \mu$$ \(\mu\)is the sample mean of the time series \( \{W_t\} \).
 * Defining the overall constant \( \theta_0 \) by \(\theta_0 := \mu(1-
 * \sum_{i=1}^3\phi_i)\), we obtain the following equivalent representation:
 * $$W_t=\theta_0+\phi_1W_{t-1}+\phi_2W_{t-2}+ \phi_3W_{t-3}+a_t\rm{.}$$ The
 * example computes estimates for
 * \(\theta_0\rm{,}\,\phi_1\rm{,}\,\phi_2\rm{,}\,\phi_3\) for each of the three
 * parameter estimation methods available.</p>
 *
 * @see <a href="ARAutoUnivariateEx1.java">Code</a>
 * @see <a href="doc-files/ARAutoUnivariateEx1.out">Output</a>
 */
public class ARAutoUnivariateEx1 {

    public static void main(String args[]) throws Exception {
        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
        };

        ARAutoUnivariate autoAR = new ARAutoUnivariate(20, z);
        System.out.println("");
        System.out.println("    Method of Moments ");
        System.out.println("");

        autoAR.setEstimationMethod(ARAutoUnivariate.METHOD_OF_MOMENTS);
        autoAR.compute();

        System.out.println("Order Selected: " + autoAR.getOrder());
        System.out.println("AIC = " + autoAR.getAIC() + "       Variance = "
                + autoAR.getInnovationVariance());
        System.out.println("Constant = " + autoAR.getConstant());
        System.out.println("");
        new PrintMatrix("AR estimates are:  ").print(autoAR.getAR());

        /* try another method */
        System.out.println("");
        System.out.println("");
        System.out.println("    Least Squares ");
        System.out.println("");
        autoAR.setEstimationMethod(ARAutoUnivariate.LEAST_SQUARES);
        autoAR.compute();

        System.out.println("Order Selected: " + autoAR.getOrder());
        System.out.println("AIC = " + autoAR.getAIC() + "       Variance = "
                + autoAR.getInnovationVariance());
        System.out.println("Constant = " + autoAR.getConstant());
        System.out.println();
        new PrintMatrix("AR estimates are:  ").print(autoAR.getAR());

        System.out.println("");
        System.out.println("");
        System.out.println("    Maximum Likelihood ");
        System.out.println("");
        autoAR.setEstimationMethod(ARAutoUnivariate.MAX_LIKELIHOOD);
        autoAR.compute();

        System.out.println("Order Selected: " + autoAR.getOrder());
        System.out.println("AIC = " + autoAR.getAIC() + "       Variance = "
                + autoAR.getInnovationVariance());
        System.out.println("Constant = " + autoAR.getConstant());
        System.out.println();
        new PrintMatrix("AR estimates are:  ").print(autoAR.getAR());
    }
}