This note presents a nonparametric sieve bootstrap method for estimating the variance of impulse response coefficients and the process steady-state gain determined via correlation analysis. The bootstrap estimates are demonstrated to be better for small samples than the analytical finite sample variance expression for the simplified form (assuming white noise input) of the Wiener-Hopf equations. Monte Carlo simulations demonstrate that solving the linear equations resulting from the Wiener-Hopf equations can result in a variance reduction.