In order to discuss spectral features of long-term solar-activity dynamics, we show in Figure 19 a
wavelet spectral decomposition of the sunspot number reconstruction throughout the Holocene shown in
Figure 17. The left-hand panels show the conventional wavelet decomposition in the time-frequency
domain, while the right-hand panels depict the global spectrum, namely, an integral over the
time domain, which is comparable to a Fourier spectrum. The peak in the global spectrum at
about an 80-year period corresponds to the Gleissberg periodicity, known from a simple Fourier
analysis of the ^{14}C series (Peristykh and Damon, 2003). The peak at an approximately
150 year period does not correspond to a persistent periodicity, but is formed by a few time
intervals (mostly 6000 – 4000 BC) and can be related to another “branch” of the secular cycle,
according to Ogurtsov et al. (2002). The de Vries/Suess cycle, with a period of about 210 years, is
prominent in the global spectrum, but it is intermittent and tends to become strong with around
2400 clustering time (Usoskin and Kovaltsov, 2004). Another variation with a period of around
350 years can be observed after 6000 BC. Variations with a characteristic time of 600 – 700 years
are intermittent and can be hardly regarded as a typical feature of solar activity. Of special
interest is the 2000 – 2400 year Hallstatt cycle (see, e.g., Vitinsky et al., 1986; Damon and
Sonett, 1991; Vasiliev and Dergachev, 2002), which is relatively stable and mostly manifests itself as a
modulation of long-term solar activity, leading to the clustering of grand minima (Usoskin
et al., 2007).

On the other hand, an analysis of the occurrence of grand minima (see Section 4.3) shows no clear periodicity except for a marginal 2400 year clustering, implying that the occurrence of grand minima and maxima is not a result of long-term cyclic variability but is defined by stochastic/chaotic processes.

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