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Autoregressive spectral estimates under ignored changes in the mean

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  • Matei Demetrescu
  • Mehdi Hosseinkouchack

Abstract

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

Suggested Citation

  • Matei Demetrescu & Mehdi Hosseinkouchack, 2022. "Autoregressive spectral estimates under ignored changes in the mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 329-340, March.
    • Handle: RePEc:bla:jtsera:v:43:y:2022:i:2:p:329-340
    DOI: 10.1111/jtsa.12612
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    References listed on IDEAS

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