apply this method when the sample is small. A method sometimes used to improve the accuracy of the estimators in finite samples is to iterate, i.e. taking the residuals from FGLS to update the errors covariance estimator, and then updating the FGLS estimation, applying the same idea iteratively until the estimators vary less than some tolerance. But this method does not necessarily improve the efficiency of the estimator very much if the original sample was small. A reasonable option when samples are not too large is to apply OLS, but throwing away the classical variance estimator (which is inconsistent in this framework) and using a HAC (Heteroskedasticity and Autocorrelation Consistent) estimator. For example, in autocorrelation context we can use the Bartlett estimator (often known as Newey–West estimator estimator since these authors popularized the use of this estimator among econometricians in their 1987 Econometrica article), and in heteroskedastic context we can use the Eicker–White estimator. This approach is much safer, and it is the appropriate path to take unless the sample is large, and "large" is sometimes a slippery issue (e.g. if the errors distribution is asymmetric the required sample would be much larger). The ordinary least squares (OLS) estimator is calculated as usual by and estimates of the residuals are constructed. For simplicity consider the model for heteroscedastic and not autocorrelated errors. Assume that the variance-covariance matrix of the error vector is diagonal, or equivalently that errors from distinct observations are uncorrelated. Then each diagonal entry may be estimated by the fitted residuals so may be constructed by It is important to notice that the squared residuals cannot be used in the previous expression; we need an estimator of the errors variances. To do so, we can use a parametric heteroskedasticity model, or a nonparametric estimator. Once this step is fulfilled, we can proceed: Estimate using using weighted least squares The procedure can be iterated. The first iteration is given by This estimation of can be iterated to convergence. Under regularity conditions any of the FGLS estimator (or that of any of its iterations, if we iterate a finite number of times) is asymptotically distributed as where n is the sample size and here p-lim means limit in probability See also Confidence region Effective degrees of freedom Prais–Winsten estimation References Further reading Least squares Estimation methods Regression with time series structure