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?
Best 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.