协整关系变点检测与统计套利实战：捕捉配对交易的黄金窗口

# CUSUM变点检测（示例代码框架）
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import coint

# 假设有一对股票价格序列
stock_a = np.log(np.random.randn(1000).cumsum() + 100)
stock_b = np.log(np.random.randn(1000).cumsum() + 100)

# 计算残差
residuals = stock_a - stock_b

# CUSUM统计量
cusum = np.cumsum(residuals - residuals.mean())
threshold = 5 * np.std(residuals) * np.sqrt(len(residuals))

# 检测变点
changepoints = np.where(np.abs(cusum) > threshold)[0]

# 初始配对筛选（示例代码框架）
import pandas as pd
from statsmodels.tsa.stattools import coint

def find_cointegrated_pairs(stocks_data):
    n = len(stocks_data.columns)
    pairs = []
    
    for i in range(n):
        for j in range(i+1, n):
            stock1 = stocks_data.iloc[:, i]
            stock2 = stocks_data.iloc[:, j]
            
            # Engle-Granger检验
            score, pvalue, _ = coint(stock1, stock2)
            
            if pvalue < 0.05:  # 协整关系显著
                pairs.append((stocks_data.columns[i], 
                             stocks_data.columns[j], 
                             pvalue))
    
    return pairs