Understanding the Periodogram and Spectral Density
The plot of the periodogram shows a sequence of peaks that stand out from the background noise, with the lowest frequency peak at a frequency of just less than 0.1. You suspect that the data contain an annual periodic component, so consider the contribution that an annual component would make to the periodogram. Each of the data points in the time series represents a month, so an annual periodicity corresponds to a period of 12 in the current data set. Because period and frequency are reciprocals of each other, a period of 12 corresponds to a frequency of 1/12 (or 0.083). So an annual component implies a peak in the periodogram at 0.083, which seems consistent with the presence of the peak just below a frequency of 0.1.
The univariate statistics table contains the data points that are used to plot the periodogram. Notice that, for frequencies of less than 0.1, the largest value in the Periodogram column occurs at a frequency of 0.08333—precisely what you expect to find if there is an annual periodic component. This information confirms the identification of the lowest frequency peak with an annual periodic component. But what about the other peaks at higher frequencies?
The remaining peaks are best analyzed with the spectral density function, which is simply a smoothed version of the periodogram. Smoothing provides a means of eliminating the background noise from a periodogram, allowing the underlying structure to be more clearly isolated.
The spectral density consists of five distinct peaks that appear to be equally spaced. The lowest frequency peak simply represents the smoothed version of the peak at 0.08333. To understand the significance of the four higher frequency peaks, remember that the periodogram is calculated by modeling the time series as the sum of cosine and sine functions. Periodic components that have the shape of a sine or cosine function (sinusoidal) show up in the periodogram as single peaks. Periodic components that are not sinusoidal show up as a series of equally spaced peaks of different heights, with the lowest frequency peak in the series occurring at the frequency of the periodic component. So the four higher frequency peaks in the spectral density simply indicate that the annual periodic component is not sinusoidal.
You have now accounted for all of the discernible structure in the spectral density plot and conclude that the data contain a single periodic component with a period of 12 months.