@MISC{Sun10nonparametricestimation, author = {Ying Sun and Jeffrey D. Hart and Marc G. Genton}, title = {Nonparametric Estimation of a Periodic Sequence}, year = {2010} }

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Abstract

A nonparametric method is proposed 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-onecycle” version of cross-validation (CV) and complements the periodogram, a typical frequency domain period estimation tool. The CV method is computationally simple and implicitly penalizes multiples of the smallest period, leading to a “virtually ” consistent estimator, which is investigated both theoretically and by simulation. Estimating a period is tantamount to selecting a model, and it is shown that the CV estimator works much better in the period estimation context than it does in other model selection problems. As applications, the CV method is demonstrated on three well-known time series: the sunspots and lynx trapping data, and the El Niño series of sea surface temperatures.