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In this paper, Cram\'{e}r type moderate deviations for the maximum of theperiodogram and its studentized version are derived. The results are thenapplied to a simultaneous testing problem in gene expression time series. It isshown that the level of the simultaneous tests is accurate provided that thenumber of genes $G$ and the sample size $n$ satisfy $G=\exp(o(n^{1/3}))$.

Cram\'{e}r Type Moderate Deviation for the Maximum of the Periodogram with Application to Simultaneous Tests in Gene Expression Time Series