第23讲：斯皮尔曼等级相关 (Spearman Rank Correlation)

import scipy.stats as stats
data = [85, 90, 78, 90, 92]
print(stats.rankdata(data, method='average'))  # [2. 3.5 1. 3.5 5.]

X = [10, 9, 5, 7, 5]
Y = [20, 17, 11, 15, 13]

# 转换等级
X_rank = [5,4,1.5,3,1.5]
Y_rank = [5,4,1,3,2]

# 计算差值平方和
d_sq = sum([(x-y)**2 for x,y in zip(X_rank,Y_rank)])  # 0.5

rho = 1 - 6*0.5/(5*(25-1))  # 0.975

import numpy as np
from scipy import stats

x = np.random.normal(size=100)
y = np.exp(x) + np.random.normal(scale=0.5, size=100)

corr, p_value = stats.spearmanr(x, y)
print(f"相关系数: {corr:.3f}, p值: {p_value:.4f}")

import yfinance as yf
import pandas as pd

# 获取标普500和道琼斯指数数据
data = yf.download(['^GSPC', '^DJI'], start='2020-01-01', end='2023-01-01')['Close']
returns = data.pct_change().dropna()

# 计算滚动三个月相关性
rolling_corr = returns.rolling(60).corr(pairwise=True).iloc[:,0,1]

# 可视化
import matplotlib.pyplot as plt
plt.figure(figsize=(10,6))
rolling_corr.plot(title='3个月滚动斯皮尔曼相关性')
plt.ylabel('相关系数')
plt.show()

# 获取股票数据
symbols = ['AAPL', 'MSFT', 'GOOG', 'AMZN', 'META']
data = yf.download(symbols, period='1y')['Close']

# 计算月度收益
monthly_returns = data.resample('M').last().pct_change()

# 生成因子（过去三个月动量）
factor = monthly_returns.rolling(3).mean().shift(1)

# 计算等级相关性
correlations = []
for i in range(3, len(monthly_returns)):
    current_factor = factor.iloc[i].rank()
    next_return = monthly_returns.iloc[i].rank()
    corr = stats.spearmanr(current_factor, next_return).correlation
    correlations.append(corr)

print(f"平均前瞻相关性: {np.mean(correlations):.3f}")

def detect_lag_correlation(x, y, max_lag=5):
    correlations = []
    for lag in range(max_lag+1):
        shifted_y = y.shift(-lag).dropna()
        common_index = x.index.intersection(shifted_y.index)
        corr = stats.spearmanr(x.loc[common_index], shifted_y.loc[common_index]).correlation
        correlations.append((lag, corr))
    return pd.DataFrame(correlations, columns=['Lag', 'Correlation'])

# 使用示例
np.random.seed(42)
x = pd.Series(np.random.rand(100))
y = x.shift(2).iloc[2:].reset_index(drop=True) + np.random.normal(scale=0.1, size=98)
results = detect_lag_correlation(x, y)
print(results.sort_values('Correlation', ascending=False))

# 练习参考答案
# 练习1：
aapl = yf.download('AAPL', period='1y')
aapl['Return'] = aapl['Close'].pct_change()
aapl['Volume'] = aapl['Volume']
corr = stats.spearmanr(aapl['Return'].dropna(), aapl['Volume'].dropna())
print(f"收益率与交易量相关性：{corr.correlation:.3f}")