Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero of some process+ Commonly used are kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR~1! regression+ However, it is known that with substantially correlated errors, the OLS estimate of the AR~1! parameter is severely biased+ In this paper, we first show that this least-squares bias induces a significant increase in the bias and

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... an-squared error~MSE! of kernel-based estimators+ We then consider a variant of the autoregressive spectral density estimator that does not share these shortcomings because it bypasses the use of the estimate from the AR~1! regression+ Simulations and local asymptotic analyses show its bias and MSE to be much smaller than those of a kernel-based estimator when there is strong negative serial correla-tion+ We also include a discussion about the appropriate choice of the truncation lag+