We study the properties of an infinite MA-representation of an autoregressive approximation for a stationary, real-valued process. In doing so we give an extension of Wiener's Theorem in the deterministic approximation set-up. When dealing with data, we can use this new key result to obtain insight into the structure of infinite MA-representations of fitted autoregressive models where the order increases with the sample size. In particular, we give a uniform bound for estimating the moving-average coefficients via autoregressive approximation being uniform over all integers.