DAY 56 时序数据的检验

作业：自行构造数据集，来检查是否符合这个要求。

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import acf, pacf, adfuller, lbtest
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.seasonal import seasonal_decompose

# 设置中文显示
plt.rcParams["font.family"] = ["SimHei", "WenQuanYi Micro Hei", "Heiti TC"]
plt.rcParams["axes.unicode_minus"] = False  # 解决负号显示问题

def generate_and_test_white_noise():
    """生成白噪声序列并进行检验"""
    # 生成白噪声序列（均值0，方差1的正态分布）
    np.random.seed(42)
    white_noise = np.random.normal(loc=0, scale=1, size=1000)
    white_noise_series = pd.Series(white_noise, name='白噪声序列')
    
    # 白噪声检验：Ljung-Box检验
    lb_test_result = lbtest(white_noise_series, nlags=10)
    print("===== 白噪声序列检验 =====")
    print(f"Ljung-Box检验P值列表：{lb_test_result.pvalues.round(4)}")
    print(f"是否全部P值>0.05：{np.all(lb_test_result.pvalues > 0.05)}")
    
    # 可视化ACF和PACF
    fig, axes = plt.subplots(1, 2, figsize=(12, 4))
    plot_acf(white_noise_series, lags=30, ax=axes[0])
    axes[0].set_title('白噪声ACF图')
    plot_pacf(white_noise_series, lags=30, ax=axes[1])
    axes[1].set_title('白噪声PACF图')
    plt.tight_layout()
    plt.savefig('white_noise_acf_pacf.png')
    plt.close()
    
    return white_noise_series

def generate_and_test_non_stationary():
    """生成非平稳序列并进行平稳性检验"""
    # 生成随机游走序列（非平稳）
    np.random.seed(42)
    random_walk = np.cumsum(np.random.normal(loc=0, scale=1, size=1000))
    random_walk_series = pd.Series(random_walk, name='随机游走序列')
    
    # 平稳性检验：ADF单位根检验
    adf_result = adfuller(random_walk_series)
    print("\n===== 随机游走序列平稳性检验 =====")
    print(f"ADF统计量：{adf_result[0]:.4f}")
    print(f"P值：{adf_result[1]:.4f}")
    print(f"1%临界值：{adf_result[4]['1%']:.4f}")
    print(f"是否拒绝原假设（非平稳）：{adf_result[1] < 0.05}")
    
    # 可视化序列
    plt.figure(figsize=(10, 4))
    plt.plot(random_walk_series)
    plt.title('随机游走序列（非平稳）')
    plt.xlabel('时间')
    plt.ylabel('值')
    plt.tight_layout()
    plt.savefig('random_walk_series.png')
    plt.close()
    
    return random_walk_series

def generate_and_test_seasonal():
    """生成季节性序列并进行季节性检验"""
    # 生成带季节性的序列：趋势+季节性+白噪声
    np.random.seed(42)
    time = np.arange(0, 1000)
    trend = 0.01 * time  # 线性趋势
    seasonality = 5 * np.sin(2 * np.pi * time / 12)  # 周期为12的季节性
    noise = np.random.normal(loc=0, scale=1, size=1000)
    seasonal_series = pd.Series(trend + seasonality + noise, name='季节性序列')
    
    # 季节性检验：ACF检验
    acf_values = acf(seasonal_series, nlags=30)
    print("\n===== 季节性序列检验 =====")
    print(f"滞后12阶ACF值：{acf_values[12]:.4f}")
    
    # 可视化ACF和序列
    fig, axes = plt.subplots(2, 1, figsize=(10, 8))
    plot_acf(seasonal_series, lags=30, ax=axes[0])
    axes[0].set_title('季节性序列ACF图')
    axes[1].plot(seasonal_series)
    axes[1].set_title('季节性序列（趋势+周期+噪声）')
    plt.tight_layout()
    plt.savefig('seasonal_series.png')
    plt.close()
    
    # 序列分解
    decomposition = seasonal_decompose(seasonal_series, model='additive', period=12)
    trend = decomposition.trend
    seasonal = decomposition.seasonal
    residual = decomposition.resid
    
    # 可视化分解结果
    fig, axes = plt.subplots(4, 1, figsize=(10, 10))
    axes[0].plot(seasonal_series)
    axes[0].set_title('原始序列')
    axes[1].plot(trend)
    axes[1].set_title('趋势成分')
    axes[2].plot(seasonal)
    axes[2].set_title('季节性成分')
    axes[3].plot(residual)
    axes[3].set_title('残差成分')
    plt.tight_layout()
    plt.savefig('seasonal_decomposition.png')
    plt.close()
    
    return seasonal_series

def main():
    """主函数：执行所有检验并汇总结果"""
    print("===== 时间序列假设检验演示 =====")
    
    # 1. 检验白噪声
    white_noise = generate_and_test_white_noise()
    
    # 2. 检验非平稳序列
    non_stationary = generate_and_test_non_stationary()
    
    # 3. 检验季节性序列
    seasonal = generate_and_test_seasonal()
    
    print("\n===== 假设检验结论 =====")
    print("1. 白噪声序列：Ljung-Box检验P值全部>0.05，不拒绝‘白噪声’原假设")
    print("2. 随机游走序列：ADF检验P值>0.05，不拒绝‘非平稳’原假设")
    print("3. 季节性序列：ACF滞后12阶显著（接近1），存在季节性")
    
    print("\n可视化图表已保存至当前目录：")
    print("- white_noise_acf_pacf.png")
    print("- random_walk_series.png")
    print("- seasonal_series.png")
    print("- seasonal_decomposition.png")

if __name__ == "__main__":
    main()