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.
Bibliographical noteFunding 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.
- Model selection
- Nonparametric estimation
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics