This paper presents a simple method for calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes the consistency of the estimated covariance matrix under general conditions. The paper discusses the estimation of the asymptotic covariance matrix for generalized method of moments (GMM) estimators, which is essential for constructing asymptotic confidence intervals and hypothesis tests. The paper introduces a new estimator for the asymptotic covariance matrix, $ \hat{S}_T $, which is positive semi-definite. This estimator is constructed using sample autocovariances and modified Bartlett weights to smooth the sample autocovariance function. The estimator is shown to be positive semi-definite because the sample autocovariance function is positive semi-definite. The paper also provides a proof of the consistency of $ \hat{S}_T $ under certain regularity conditions. These conditions include the measurability and differentiability of the functions involved, the boundedness of the moments of the functions, and the mixing properties of the data. The consistency of $ \hat{S}_T $ is shown to hold under the assumption that the number of nonzero autocorrelations, m, grows more slowly than $ T^{1/4} $ as the sample size T increases. The paper also discusses the implications of the positive semi-definiteness of $ \hat{S}_T $ for the formation of asymptotic confidence intervals and hypothesis tests. It notes that an estimator of $ \hat{S}_T $ that is not positive semi-definite may lead to negative estimated variances and test statistics, which can be problematic for inference. The paper also suggests that the use of time domain techniques for estimating $ \hat{S}_T $ can be useful, as they are simple to compute and can be used to construct positive semi-definite estimators of the asymptotic covariance matrix.This paper presents a simple method for calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes the consistency of the estimated covariance matrix under general conditions. The paper discusses the estimation of the asymptotic covariance matrix for generalized method of moments (GMM) estimators, which is essential for constructing asymptotic confidence intervals and hypothesis tests. The paper introduces a new estimator for the asymptotic covariance matrix, $ \hat{S}_T $, which is positive semi-definite. This estimator is constructed using sample autocovariances and modified Bartlett weights to smooth the sample autocovariance function. The estimator is shown to be positive semi-definite because the sample autocovariance function is positive semi-definite. The paper also provides a proof of the consistency of $ \hat{S}_T $ under certain regularity conditions. These conditions include the measurability and differentiability of the functions involved, the boundedness of the moments of the functions, and the mixing properties of the data. The consistency of $ \hat{S}_T $ is shown to hold under the assumption that the number of nonzero autocorrelations, m, grows more slowly than $ T^{1/4} $ as the sample size T increases. The paper also discusses the implications of the positive semi-definiteness of $ \hat{S}_T $ for the formation of asymptotic confidence intervals and hypothesis tests. It notes that an estimator of $ \hat{S}_T $ that is not positive semi-definite may lead to negative estimated variances and test statistics, which can be problematic for inference. The paper also suggests that the use of time domain techniques for estimating $ \hat{S}_T $ can be useful, as they are simple to compute and can be used to construct positive semi-definite estimators of the asymptotic covariance matrix.