The asymptotic properties of the bootstrap in the frequency domain based on Studentized periodogram ordinates are studied. It is proved that this bootstrap approximation is valid for ratio statistics such as autocorrelations. By using Edgeworth expansions it is shown that the bootstrap approximation even outperforms the normal approximation. The results carry over to Whittle estimates. In a simulation study the behavior of the bootstrap is studied for empirical correlations and Whittle estimates.
"A frequency domain bootstrap for ratio statistics in time series analysis." Ann. Statist. 24 (5) 1934 - 1963, October 1996. https://doi.org/10.1214/aos/1069362304