Summary: A new methodology for optimal linear prediction of a stationary time series is introduced. Given a sample \(X_{1},\dots,X_{n}\), the optimal linear predictor of \(X_{n+1}\) is \(\tilde{X}_{n+1}=\phi_{1}(n)X_{n}+\phi_{2}(n)X_{n-1}+\cdots+\phi_{n}(n)X_{1}\). In practice, the coefficient vector \(\phi(n)\equiv(\phi_{1}(n),\phi_{2}(n),\dots,\phi_{n}(n))'\) is routinely truncated to its first \(p\) components in order to be consistently estimated. By contrast, we employ a consistent estimator of the \(n\times n\) autocovariance matrix \(\Gamma_{n}\) in order to construct a consistent estimator of the optimal, full-length coefficient vector \(\phi(n)\). Asymptotic convergence of the proposed predictor to the oracle is established, and finite sample simulations are provided to support the applicability of the new method. As a by-product, new insights are gained on the subject of estimating \(\Gamma_{n}\) via a positive definite matrix, and four ways to impose positivity are introduced and compared. The closely related problem of spectral density estimation is also addressed.