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Paper No. 11-01

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MJ Costa, BF Finkenstadt and PD Gould

Estimating Periodicity of Oscillatory Time Series through Resampling Techniques

Abstract: Accurate estimation of the period length of time-course data from cyclical biological processes, such as those driven by the endogenous circadian pacemaker, is crucial for making inferences about the properties of the biological clock found in many living organisms. In this paper we propose a methodology that combines spectral analysis with resampling techniques termed spectrum resampling (SR). Extensive numerical studies show that SR is superior and considerably more robust to non-sinusoidal patterns than currently available methods based on Fourier approximations, namely the FFT-NLLS method by Plautz et al. (1997, Journal of Biological Rhythms 12, 204-217). We also develop a nonparametric test for testing for changes in period length. The test uses resampling techniques and allows for period estimates with different variances. Simulation studies show that it attains correct nominal size and has good power properties when compared to parametric alternatives. The proposed SR method and statistical test are illustrated with real data examples.

Keywords: Circadian rhythms; Hypotheses tests; Period estimation; Resampling; Spectrum.