加权最小二乘法（weighted least square，WLS）回归。

OLS是minimize sum(residuals^2),而WLS是minimize sum(w*residuals^2),即将权数与残差平方相乘后再求和，所以要先定义权重。

1. WLS 加权回归

import statsmodels.api as sm 

x = factor0_market2

y = returns0_market2

model = sm.WLS(y, x, weights=weight1).fit()

z = model.params[:]

barra_returns.loc[:, this_day[i]] = z

x：

 

y：

 

weight1：