# Newey–West estimator

A Newey–West estimator is used in statistics and econometrics to provide an estimate of the covariance matrix of the parameters of a regression-type model when this model is applied in situations where the standard assumptions of regression analysis do not apply.[1] It was devised by Whitney K. Newey and Kenneth D. West in 1987, although there are a number of later variants.[2][3][4][5] The estimator is used to try to overcome autocorrelation, or correlation, and heteroskedasticity in the error terms in the models. This is often used to correct the effects of correlation in the error terms in regressions applied to time series data.

The problem in autocorrelation, often found in time series data, is that the error terms are correlated over time. This can be demonstrated in $Q*$, a matrix of sums of squares[disambiguation needed] and cross products that involves $\sigma_{(ij)}$ and the rows of $X$. The least squares estimator $b$ is a consistent estimator of $\beta$. This implies that the least squares residuals $e_i$ are "point-wise" consistent estimators of their population counterparts $E_i$. The general approach, then, will be to use $X$ and $e$ to devise an estimator of $Q*$.[6] What this means is that as the time between error terms increases, the correlation between the error terms decreases. The estimator thus can be used to improve the ordinary least squares (OLS) regression when the variables have heteroskedasticity or autocorrelation.

$w_\ell=1 - \frac{\ell}{L+1}$