Newey-West standard errors for OLS in Python?
I want to have a coefficient and Newey-West standard error associated with it.
I am looking for Python library (ideally, but any working solutions is fine) that can do what the following R code is doing:
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)
Result:
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
I get the coefficients and associated with them standard errors.
I see statsmodels.stats.sandwich_covariance.cov_hac module, but I don't see how to make it work with OLS.
Answer
Edited (10/31/2015) to reflect preferred coding style for statsmodels as fall 2015.
In statsmodels version 0.6.1 you can do the following:
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
Or you can use the get_robustcov_results method after fitting the model:
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
The defaults for statsmodels are slightly different than the defaults for the equivalent method in R. The R method can be made equivalent to the statsmodels default (what I did above) by changing the vcov, call to the following:
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
You can also still do Newey-West in pandas (0.17), although I believe the plan is to deprecate OLS in pandas:
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---------------------------------