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 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] This means 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.

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

References

1. ^
2. ^ Newey, Whitney K; West, Kenneth D (1987). "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix". Econometrica 55 (3): 703–708. doi:10.2307/1913610. JSTOR 1913610.
3. ^ Andrews, Donald W. K. (1991). "Heteroskedasticity and autocorrelation consistent covariance matrix estimation". Econometrica 59 (3): 817–858. doi:10.2307/2938229. JSTOR 2938229.
4. ^ Newey, Whitney K.; West, Kenneth D. (1994). "Automatic lag selection in covariance matrix estimation". Review of Economic Studies 61 (4): 631–654. doi:10.2307/2297912. JSTOR 2297912.
5. ^ Smith, Richard J. (2005). "Automatic positive semidefinite HAC covariance matrix and GMM estimation". Econometric Theory 21 (1): 158–170. doi:10.1017/S0266466605050103.
6. ^ Greene, William H. (1997). Econometric Analysis (3rd ed.).