An approach to bootstrapping kernel spectral density estimates is described which is based on resampling from the periodogram of the original data. We show that it is asymptotically valid under suitable conditions, and we illustrate its performance for a medium-sized time series sample with a small simulation study.
"On Bootstrapping Kernel Spectral Estimates." Ann. Statist. 20 (1) 121 - 145, March, 1992. https://doi.org/10.1214/aos/1176348515