Nonlinear Modeling of El Nino/Southern Oscillation Index

Abstract

The southern oscillation index (SOI) series which is associated with El Nino was modeled as a linear stochastic model in the previous study. We also assume that it has a linear characteristic and is fitted to an autoregressive/moving average (ARMA) type model. The Bayesian information criterion is used for determining appropriate order of ARMA model and ARMA(1,8; 1) is chosen for the SOI series. The model is verified from the autocorrelation function, the partial autocorrelation function, and Porte Manteau test on the residuals for its validity. However, the hypothesis of randomness on the residual is rejected from a new test technique, called the Brock–Dechert–Scheinkman (BDS) statistic, which can detect the nonlinearity of time series that could not be determined by the conventional test techniques. This means that the ARMA model is not appropriate for the SOI series and this may be due to the nonlinearity of the time series. Therefore, we assume that the SOI series may have nonlinear properties and consider nonlinear modeling for the series. We use the close returns plot for searching for chaos, which has the nonlinear deterministic characteristics of a time series and found that there is no evidence of deterministic chaos in the SOI series. Therefore, we can consider that the nonlinear stochastic models may be more valid for the SOI series. The SOI series is fitted to the autoregressive conditional heteroscedasticity type model which has a nonlinear stochasticity and the model is tested on the residuals for its validity by the BDS statistic. As a result, the fitted nonlinear stochastic model is appropriate for the modeling of the SOI series and we may conclude that the nonlinear stochastic model is more valid for the SOI time series analysis and modeling than linear stochastic analog.