Spectrum Analysis Basic Notation and Principles - Results when no Periodicity in the Series Exists
Finally, what if there are no recurring cycles in the data, that is, if each observation is completely independent of all other observations? If the distribution of the observations follows the normal distribution, such a time series is also referred to as a white noise series (like the white noise you hear on the radio when tuned in between stations). A white noise input series will result in periodogram values that follow an exponential distribution. Thus, by testing the distribution of periodogram values against the exponential distribution, one may test whether the input series is different from a white noise series. The Time Series module will produce a histogram of the periodogram values, and fit the exponential distribution to the histogram. In addition, you can also compute the Kolmogorov-Smirnov one-sample d statistic (see Distribution Fitting for more details).
Testing for white noise in certain frequency bands
Note that you can also plot the periodogram values for a particular frequency range only. Again, if the input is a white noise series with respect to those frequencies (i.e., it there are no significant periodic cycles of those frequencies), then the distribution of the periodogram values should again follow an exponential distribution.