This paper presents a method for calculating a heteroskedasticity and autocorrelation consistent (HAC) covariance matrix that is positive semi-definite by construction. The authors, Whitney K. Newey and Kenneth D. West, establish the consistency of the estimated covariance matrix under general conditions. They propose an estimator of the asymptotic covariance matrix, which is crucial for constructing asymptotic confidence intervals and hypothesis tests. The paper discusses the challenges in estimating the matrix and introduces a time domain approach to ensure positive semi-definiteness. The authors also provide theoretical results and proofs to support their method, including a theorem on the consistency of the estimator and another on the conditions under which the estimator converges. The paper is part of the NBER's research program in Economic Fluctuations and is revised from a previous version.This paper presents a method for calculating a heteroskedasticity and autocorrelation consistent (HAC) covariance matrix that is positive semi-definite by construction. The authors, Whitney K. Newey and Kenneth D. West, establish the consistency of the estimated covariance matrix under general conditions. They propose an estimator of the asymptotic covariance matrix, which is crucial for constructing asymptotic confidence intervals and hypothesis tests. The paper discusses the challenges in estimating the matrix and introduces a time domain approach to ensure positive semi-definiteness. The authors also provide theoretical results and proofs to support their method, including a theorem on the consistency of the estimator and another on the conditions under which the estimator converges. The paper is part of the NBER's research program in Economic Fluctuations and is revised from a previous version.