Many cellular processes exhibit periodic behaviors. Hence, one of the important tasks in gene expression data analysis is to detect subset of genes that exhibit cyclicity or periodicity in their gene expression time series profiles. Unfortunately, gene expression time series profiles are usually of very short length and highly contaminated with noise. This makes detection of periodic profiles a very difficult problem. Recently, a hypothesis testing method based on the Fisher g-statistic with correction for multiple testing has been proposed to detect periodic gene expression profiles. However, it was observed that the test is not reliable if the signal length is too short. In this paper, we performed extensive simulation study to investigate the statistical power of the test as a function of signal length, SNR, and the false discovery rate. We found that the number of periodic profiles can be severely underestimated for short length signal. The findings indicated that caution needs to be exercised when interpreting the test result for very short length signals.