Python中如何计算OLS的Newey-West标准误差？

Question

我想要一个系数和与之相关的Newey-West标准误差。

我在寻找一个Python库（最好是这样，但任何有效的解决方案都可以），它能做到以下R代码所做的事情：

library(sandwich)
library(lmtest)

a <- matrix(c(1,3,5,7,4,5,6,4,7,8,9))
b <- matrix(c(3,5,6,2,4,6,7,8,7,8,9))

temp.lm = lm(a ~ b)

temp.summ <- summary(temp.lm)
temp.summ$coefficients <- unclass(coeftest(temp.lm, vcov. = NeweyWest))

print (temp.summ$coefficients)

结果：

             Estimate Std. Error   t value  Pr(>|t|)
(Intercept) 2.0576208  2.5230532 0.8155281 0.4358205
b           0.5594796  0.4071834 1.3740235 0.2026817

我得到了系数以及与它们相关的标准误差。

我看到有一个叫做 statsmodels.stats.sandwich_covariance.cov_hac 的模块，但我不知道怎么把它和OLS结合起来使用。

Answer 1

编辑于2015年10月31日，以反映2015年秋季对statsmodels的首选编码风格。

在statsmodels版本0.6.1中，你可以这样做：

import pandas as pd
import numpy as np
import statsmodels.formula.api as smf

df = pd.DataFrame({'a':[1,3,5,7,4,5,6,4,7,8,9],
                   'b':[3,5,6,2,4,6,7,8,7,8,9]})

reg = smf.ols('a ~ 1 + b',data=df).fit(cov_type='HAC',cov_kwds={'maxlags':1})
print(reg.summary())

                                OLS Regression Results
==============================================================================
Dep. Variable:                      a   R-squared:                       0.281
Model:                            OLS   Adj. R-squared:                  0.201
Method:                 Least Squares   F-statistic:                     1.949
Date:                Sat, 31 Oct 2015   Prob (F-statistic):              0.196
Time:                        03:15:46   Log-Likelihood:                -22.603
No. Observations:                  11   AIC:                             49.21
Df Residuals:                       9   BIC:                             50.00
Df Model:                           1
Covariance Type:                  HAC
==============================================================================
                 coef    std err          z      P>|z|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept      2.0576      2.661      0.773      0.439        -3.157     7.272
b              0.5595      0.401      1.396      0.163        -0.226     1.345
==============================================================================
Omnibus:                        0.361   Durbin-Watson:                   1.468
Prob(Omnibus):                  0.835   Jarque-Bera (JB):                0.331
Skew:                           0.321   Prob(JB):                        0.847
Kurtosis:                       2.442   Cond. No.                         19.1
==============================================================================

Warnings:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction

或者，在模型拟合后，你可以使用get_robustcov_results方法：

reg = smf.ols('a ~ 1 + b',data=df).fit()
new = reg.get_robustcov_results(cov_type='HAC',maxlags=1)
print(new.summary())


                                OLS Regression Results
==============================================================================
Dep. Variable:                      a   R-squared:                       0.281
Model:                            OLS   Adj. R-squared:                  0.201
Method:                 Least Squares   F-statistic:                     1.949
Date:                Sat, 31 Oct 2015   Prob (F-statistic):              0.196
Time:                        03:15:46   Log-Likelihood:                -22.603
No. Observations:                  11   AIC:                             49.21
Df Residuals:                       9   BIC:                             50.00
Df Model:                           1
Covariance Type:                  HAC
==============================================================================
                 coef    std err          z      P>|z|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept      2.0576      2.661      0.773      0.439        -3.157     7.272
b              0.5595      0.401      1.396      0.163        -0.226     1.345
==============================================================================
Omnibus:                        0.361   Durbin-Watson:                   1.468
Prob(Omnibus):                  0.835   Jarque-Bera (JB):                0.331
Skew:                           0.321   Prob(JB):                        0.847
Kurtosis:                       2.442   Cond. No.                         19.1
==============================================================================

Warnings:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction

statsmodels的默认设置和R中相应方法的默认设置稍有不同。如果你想让R的方法和statsmodels的默认设置（我上面做的那样）相同，可以把vcov,的调用改成下面这样：

temp.summ$coefficients <- unclass(coeftest(temp.lm, 
               vcov. = NeweyWest(temp.lm,lag=1,prewhite=FALSE)))
print(temp.summ$coefficients)

             Estimate Std. Error   t value  Pr(>|t|)
(Intercept) 2.0576208  2.6605060 0.7733945 0.4591196
b           0.5594796  0.4007965 1.3959193 0.1962142

你仍然可以在pandas（0.17）中使用Newey-West方法，尽管我相信计划是逐步淘汰pandas中的OLS：

print(pd.stats.ols.OLS(df.a,df.b,nw_lags=1))

-------------------------Summary of Regression Analysis-------------------------

Formula: Y ~ <x> + <intercept>

Number of Observations:         11
Number of Degrees of Freedom:   2

R-squared:         0.2807
Adj R-squared:     0.2007

Rmse:              2.0880

F-stat (1, 9):     1.5943, p-value:     0.2384

Degrees of Freedom: model 1, resid 9

-----------------------Summary of Estimated Coefficients------------------------
      Variable       Coef    Std Err     t-stat    p-value    CI 2.5%   CI 97.5%
 --------------------------------------------------------------------------------
             x     0.5595     0.4431       1.26     0.2384    -0.3090     1.4280
     intercept     2.0576     2.9413       0.70     0.5019    -3.7073     7.8226
*** The calculations are Newey-West adjusted with lags     1

---------------------------------End of Summary---------------------------------