In this paper we compare two commonly used methods for estimation of correlation functions, the periodogram (or correlogram) method and the Welch’s method, and show that they are statistically equal. The random error in the correlation estimate is then illustrated and the effect it has on damping estimates is demonstrated by using Prony’s method on data for a simulated single-degree-of-freedom system. It is demonstrated that adding more correlation lag values does not necessarily improve the damping estimate.