Automatic local smoothing for spectral density estimation

Jianqing Fan, Eva Kreutzberger

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


This article uses local polynomial techniques to fit Whittle's likelihood for spectral density estimation. Asymptotic sampling properties of the proposed estimators are derived, and adaptation of the proposed estimator to the boundary effect is demonstrated. We show that the Whittle likelihood-based estimator has advantages over the least-squares based log-periodogram. The bandwidth for the Whittle likelihood-based method is chosen by a simple adjustment of a bandwidth selector proposed in Fan & Gijbels (1995). The effectiveness of the proposed procedure is demonstrated by a few simulated and real numerical examples. Our simulation results support the asymptotic theory that the likelihood based spectral density and log-spectral density estimators are the most appealing among their peers.

Original languageEnglish (US)
Pages (from-to)359-369
Number of pages11
JournalScandinavian Journal of Statistics
Issue number2
StatePublished - Jun 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Bandwidth selection
  • Local polynomial fit
  • Periodogram
  • Spectral density estimation
  • Whittle likelihood


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