This study analyzes the variance ratio test in the frequency domain. Using the concept of the summation filter, its formulation is clearer in the frequency domain rather than in the time domain. We can formulate the variance ratio and explain its implications in the frequency domain. Two applications of the spectral analysis are presented. First, we try to explain the low power problem of the random walk hypothesis, suggested by Summers (1986). It is due to that AR(1) alternative hypothesis is not identifiable with the random walk null hypothesis in formulating the persistent transitory component. Second, we analyze the applicability of the technical methods such as the moving average analysis. It is shown that the variance ratio can be used in selecting cycles with the appropriate period.