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Abstract

1. MacDonald, G.J., 1989. Spectral analysis of time series generated by nonlinear processes. Rev. Geophys., 27: 449–469.

For nonlinear regions prior to the onset of chaos, the periodogram offers many advantages in analyzing the spectral characteristics of a time series. The periodogram is an optimal detector, in the maximum likelihood sense of determining the frequencies of interacting oscillators. Periodogram analysis can be extended to situations in which samples are taken at uneven intervals. - The methods of spectral analysis based on generalized linear models such as maximum entropy are inappropriate for dealing with deterministic systems in the presence of noise. The statistical validity of peaks obtained by linear, parametric modeling is not well understood. - The first half of the paper gives a theoretical review, while the second half presents periodogram analyses of Earth’s obliquity, sunspots, and atmospheric carbon dioxide levels (obliquity=the angle of tilt of the Earth’s axis of rotation on the ecliptic).

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