Nonparametric inference for periodic sequences

Ying Sun*, Jeffrey D. Hart, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


This article proposes a nonparametric method for estimating the period and values of a periodic sequence when the data are evenly spaced in time. The period is estimated by a "leave-out-one-cycle" version of cross-validation (CV) and complements the periodogram, a widely used tool for period estimation. The CV method is computationally simple and implicitly penalizes multiples of the smallest period, leading to a "virtually" consistent estimator of integer periods. This estimator is investigated both theoretically and by simulation.We also propose a nonparametric test of the null hypothesis that the data have constantmean against the alternative that the sequence of means is periodic. Finally, our methodology is demonstrated on three well-known time series: the sunspots and lynx trapping data, and the El Niño series of sea surface temperatures.

Original languageEnglish (US)
Pages (from-to)83-96
Number of pages14
Issue number1
StatePublished - Feb 2012
Externally publishedYes

Bibliographical note

Funding Information:
Professor Hart’s research was supported in part by NSF grant DMS-0604801. Professor Genton’s research was partially supported by NSF (National Science Foundation) grant DMS-1007504, and award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia.


  • Consistency
  • Cross-validation
  • Model selection
  • Nonparametric estimation
  • Period

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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