Fig. 6

Power spectrum of log (ϕ_GSN) and ϕ_GSN approximated by our tuned covariance function. a Compares the power spectrum of log(ϕ_GSN) (black line, standardized to have mean = 0 and variance = 1) with the theoretical spectral density of the tuned covariance function (red line). The tuning periods are highlighted with light red shading. Panel b compares the power spectrum of ϕ_GSN (black line, standardized to have mean = 0 and variance = 1) with power spectrums of two random realizations (color lines) generated by the tuned covariance function for the period from 1610 to 2015 CE. The light red envelop indicates the estimated 95% confidence interval of the power spectrums from 1000 random realizations. c Is similar to panel b, but shows the power spectrum of a 9-year moving average version of ϕ_GSN (black lines) and the power spectra of 1000 random realizations generated by the adapted covariance matrix (see text) for the same time period. All of the power spectra were computed with the Multitaper Method (bandwidth NΩ = 8, tapers K = 8)