Spectral Estimation from Time Series Models with Relevance to the Southern Oscillation

Abstract

Abstract The theoretical spectra of certain parametric time series models with relevance to the Southern Oscillation (SO) are determined and compared with those based on a frequency-domain approach. Consistent spectral estimates are found for the two models selected in our earlier studies of the SO. All these results yield larger power at low frequencies and a dominant peak around 3–4 yr. Some reasons are offered for the slightly different behavior of the spectra as derived from the time-domain and frequency-domain approaches. For the sake of comparison, the spectra of other simpler time series models are also calculated. While larger power is found at low frequencies, no spectral peak exists in these simpler models. Some implications of the quasi-periodic behavior found in the more complex models (i.e., an intermediate peak in the spectrum) are discussed in the context of the persistence and forecasting of the SO.