We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.
"Monotone spectral density estimation." Ann. Statist. 39 (1) 418 - 438, February 2011. https://doi.org/10.1214/10-AOS804