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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 anddoi:10.1017/s0266466698145024 fatcat:la7g4nmfefee7lxmpxgrzifr5u