Autoregressive spectral estimates under ignored changes in the mean

Periodogram-based-40 estimators of the spectral density are known to exhibit distorted behavior in neighborhoods origin case so-called low frequency contamination, mimicking long-range dependence. This note quantifies estimator based on autoregressive approximations order increasing with sample size. Not surprisingly, is not consistent at under ignored changes mean, but turns out be non-zero frequencies. We furthermore show how a specific trimming fitted long autoregression can used restore consistency vicinity origin.