# Does Newey-West standard errors affects the significance level of R2?

General question: I use the linear regressions with the OLS method to check whether cross-sectional standard deviation is able to describe future sumed excess returns or not.

Because of autocorrelation there is the need to update the summary with newey west standard errors.

After updateting the t-statistics changed dramatically, but the f-statistic (required to determine the significance level of r^2) didnt change.

Is there any impact on the f-statistic by using newey-west standard errors?

## 1 Answer

Simply put, no. Standard errors are not used to calculate either the $R^2$ statistic or the $F$-statistic. $$R^2 = 1 - \dfrac{Sum\ of\ squared\ errors}{Total\ sum\ of\ squares} = 1 -\dfrac{\sum(Y - \hat Y)^2}{\sum(Y- \bar Y)^2}.$$ The $F$-statistic is the ratio of the mean squares of the model to the mean square of the residuals: $$F = \dfrac{MSM}{MSE} = \dfrac{\frac{\sum(Y - \bar Y)^2}{p - 1}}{\frac{\sum(Y - \hat Y)^2}{n-p-1}}.$$ Since neither involves the variance-covariance matrix or the standard errors of the coefficients, the Newey-West adjustment won't impact the $R^2$ or $F$-stat.

I should add that it is preferable to use the Wald test rather than the $F$-test, under conditions of heteroskedasticity and autocorrelation. See a blog post "F-tests Based on the HC or HAC Covariance Matrix Estimators" by Dave Giles.

• Thank you paqmo! Because i was told that the variance of the residuals is a required input parameter for the t- and f-statsitics and therefore newey-west affects both. – Bruno Nov 24 '16 at 17:03
• In a sense, that is true, but the f-stat concerns with the model as a whole, while standard errors concern the precision of each individual estimates of the coefficients for the terms of the model. So variance of the residuals is adjusted by the variance-covariance of the model terms. Newey-West estimators adjust how the standard errors of the regression coefficients are calculated, but not the standard error of the model (eg. square root of the mean square error). Under normal conditions, the MSE is used to scale the variance-covariance matrix, but not when robust SEs are calculated. – paqmo Nov 24 '16 at 22:16