Newey-West Estimator

Definition

${\widehat{\mathrm{Var}}}_{HAC}(\hat{\beta })={\widehat{\mathrm{Var}}}_{HCE}(\hat{\beta }){\hat{f}}_T=\frac{T{\sum }_{t=1}^T(x_t-\bar{x}){\hat{e}}_t^2}{(T-K)({\sum }_{t=1}^T(x-\bar{x}{)}^2{)}^2}\left(1+2{\sum }_{j=1}^{T-1}\left(\frac{T-j}{T}{\hat{\rho }}_j\right)\right)$ where ${\hat{\rho }}_j$ is an estimator of ${\rho }_j$, $T$ is the number of observations, and $K$ is the number of explanatory variables

A Newey-West Estimator is used to improve the OLS when the residuals are heteroskedastic or autocorrelated. It is a modification of Heteroskedasticity-Consistent Estimator