Many unit root and cointegration tests require an estimate of thespectral density function at frequency zero of some process.Commonly used are kernel estimators based on weighted sums ofautocovariances constructed using estimated residuals from an AR(1)regression. However, it is known that with substantially correlatederrors, the OLS estimate of the AR(1) parameter is severely biased.In this paper, we first show that this least-squares bias induces asignificant increase in the bias and mean-squared error (MSE) ofkernel-based estimators. We then consider a variant of theautoregressive spectral density estimator that does not share theseshortcomings because it bypasses the use of the estimate from theAR(1) regression. Simulations and local asymptotic analyses show itsbias and MSE to be much smaller than those of a kernel-basedestimator when there is strong negative serial correlation. We alsoinclude a discussion about the appropriate choice of the truncationlag.