Spectral Analysis and Filtering
Robert H. Shumway, David S. Stoffer · 2019
The cyclic behavior of data is the focus of this and the next chapter. For example, the predominant frequency in the monthly SOI series shown in Figure 1.5 is one cycle per year or 1 cycle every 12 months, ω = 1/12 cycles per observation. This is the obvious hot in the summer, cold in the winter cycle. The El Niño cycle seen in the preliminary analyses of Section 3.3 is approximately 1 cycle every 4 years (48 months), or ω = 1 /48 cycles per observation. The period of a time series is defined as the number of points in a cycle, 1/ ω . Hence, the predominant period of the SOI series is 12 months per cycle or 1 year per cycle. The El Niño period is about 48 months or 4 years.