We predicted the extreme values of the ENSO index,
the Niño3.4 index, and the Southern Oscillation Index (SOI) using extreme value theory. Various diagnostic plots for assessing the accuracy of the Generalized Pareto (GP) model fitted to the Niño3.4 index and SOI are shown, and all four
diagnostic plots support the fitted GP model. Because the shape parameter of
the Niño3.4 was negative, the Niño3.4 index had a finite upper limit. In
contrast, that of the SOI was zero, therefore the SOI did not have a finite
upper limit, and there is a possibility that a significant risk will occur. We
predicted the maximum return level for the return periods of 10, 20, 50, 100,
350, and 500 years and their respective 95% confidence intervals, CI. The
10-year, and 100-year return levels for Niño3.4 were estimated to be 2.41, and
2.62, with 95% CI [2.22, 2.59], and [2.58, 2.66], respectively. The Ni
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