ARIMA实现 java

ARIMA实现 Java

ARIMA（AutoRegressive Integrated Moving Average）是一种常用的时间序列预测方法，可以用于对未来的趋势进行预测。在本文中，我们将介绍如何使用Java实现ARIMA模型，并提供代码示例。

ARIMA简介

ARIMA模型是由自回归（AR）、差分（I）、移动平均（MA）三部分组成的，它是根据时间序列的历史数据来预测未来的值。ARIMA模型的一般形式可以表示为ARIMA(p,d,q)，其中p表示自回归阶数，d表示差分阶数，q表示移动平均阶数。

ARIMA模型的建立分为三个步骤：模型拟合、模型诊断和模型预测。在模型拟合阶段，我们需要对时间序列数据进行差分处理，以消除非平稳性；然后，通过自相关函数（ACF）和偏自相关函数（PACF）来确定模型的阶数；最后，使用最小二乘法进行模型参数的估计。

ARIMA实现

下面是一个简单的ARIMA模型实现的代码示例：

import org.apache.commons.math3.stat.regression.OLSMultipleLinearRegression;

public class ARIMA {
    private double[] data;
    private int p;
    private int d;
    private int q;

    public ARIMA(double[] data, int p, int d, int q) {
        this.data = data;
        this.p = p;
        this.d = d;
        this.q = q;
    }

    public double[] forecast(int steps) {
        double[] forecastData = new double[steps];
        // 差分处理
        double[] diffData = difference(data, d);
        // 计算AR、MA系数
        double[] arCoefficients = computeARCoefficients(diffData, p);
        double[] maCoefficients = computeMACoefficients(diffData, q);
        // 拟合ARIMA模型
        double[] arimaCoefficients = fitARIMAModel(diffData, arCoefficients, maCoefficients, p, q);
        // 预测未来值
        for (int i = 0; i < steps; i++) {
            double forecastValue = arimaCoefficients[0];
            for (int j = 1; j <= p; j++) {
                forecastValue += arimaCoefficients[j] * diffData[diffData.length - j];
            }
            for (int j = 1; j <= q; j++) {
                forecastValue += arimaCoefficients[p + j] * forecastData[i - j];
            }
            forecastData[i] = forecastValue;
            diffData = shift(diffData, forecastValue);
        }
        return forecastData;
    }

    private double[] difference(double[] data, int d) {
        double[] diffData = data.clone();
        for (int i = 0; i < d; i++) {
            for (int j = diffData.length - 1; j > 0; j--) {
                diffData[j] -= diffData[j - 1];
            }
        }
        return diffData;
    }

    private double[] computeARCoefficients(double[] data, int p) {
        double[] arCoefficients = new double[p + 1];
        OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression();
        double[][] x = new double[data.length - p][p];
        double[] y = new double[data.length - p];
        for (int i = 0; i < data.length - p; i++) {
            for (int j = 0; j < p; j++) {
                x[i][j] = data[i + p - j - 1];
            }
            y[i] = data[i + p];
        }
        regression.newSampleData(y, x);
        double[] coefficients = regression.estimateRegressionParameters();
        System.arraycopy(coefficients, 0, arCoefficients, 1, p);
        return arCoefficients;
    }

    private double[] computeMACoefficients(double[] data, int q) {
        double[] maCoefficients = new double[q + 1];
        OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression();
        double[][] x = new double[data.length - q][q];
        double[] y = new double[data.length - q];
        for (int i = 0; i < data.length - q; i++) {
            for (int j = 0; j < q; j++) {
                x[i][j] = data[i + q - j - 1];
            }
            y[i] = data[i + q];
        }
        regression.newSampleData(y, x);
        double[] coefficients = regression.estimateRegression