Significance-testing of periodogram for short time series

Periodicity detection in timecourse gene expression data is usually based on periodogram method and a pre-defined significance threshold. Existing periodogram significance testing formulae are often inaccurate for short time series. We demonstrate that the magnitude of the error resulting from using the theoretical approximations is not negligible in such case and discuss how it depends on different factors. Our conclusions are illustrated by examples of short time series typically produced by microarray studies. In these examples, we show a substantial discrepancy between different theoretical formulae and results of numerical simulations in the number of periodic genes found. We demonstrate that the accuracy of simulations is much higher than that of any of the theoretical approximations and conclude that estimation of significance should be based on comparisons with simulated datasets rather than theoretical approximations whenever feasible.