Forecasting the Southern Oscillation is a problem with a century-long history: crops, floods, and droughts from Australia to South Africa depend on it. Classic autoregressive models (ARMA) are well understood, but they are linear and fail to capture complex cycles in the data. Neural networks can handle nonlinearity, but building reliable forecast intervals for them is difficult and expensive. Alongside this work on the archive are studies where AI learns from weather data and gravitational waves, but no one had tried BART for time series. This article fills that niche.
The author used monthly SOI values from January 1876 to August 2009, totaling 1603 observations. BART sums many small decision trees, each explaining only a small part of the variability. The trees are built randomly using MCMC (Markov chain Monte Carlo), and a strong prior prevents them from growing too large. For variable selection, a built-in BART technique was used: the number of trees was reduced to 20, forcing the model to choose only useful lags. Accuracy was evaluated on a random test sample (20–33% of the data), averaging results over ten runs.
When forecasting the October SOI value from previous months, the best model used only five lags (from May to September). On the training sample, correlation reached 0.90; on the test sample, 0.81, with a mean absolute error of 4.89 and RMSE of 5.90. Excluding September to forecast two months ahead drops the correlation to 0.66. In an autoregressive setup (forecasting 1–12 months ahead), BART with five lags gave a correlation of 0.647 for one month and 0.218 for twelve months. The linear AR(5) model on the same data performed worse: 0.620 for one month and 0.112 for twelve. After five months, BART forecasts degenerate into an almost constant value with small variance.
This work demonstrates for the first time that BART is applicable to time series and outperforms ARMA in point forecast accuracy, though it does not solve the problem of long-term decay. Unlike neighboring works where neural networks are trained on huge datasets, here a Bayesian nonparametric method is used with a full uncertainty distribution. This opens the door to nonlinear modeling of climate indices without the complex tuning of neural networks.
The method can be extended to other climate series: ocean temperature, precipitation indices, river runoff. The key challenge is to build forecast intervals several steps ahead without distributed computing. Perhaps variants of BART for sequential data or hybrids with state-space models could help.
The results are useful for hydrologists, agrometeorologists, and climate risk specialists who need nonlinear forecasts with uncertainty estimates. The method may also interest statisticians working with nonstationary series.
It is worth testing BART on other indices (e.g., PDO or NAO) and comparing it with modern nonlinear methods. A separate task is to speed up the computation of forecast intervals.
For time series statistics, an open question remains: how to build reliable forecast intervals for nonlinear models without huge computational costs. This work shows that Bayesian trees give honest one-step uncertainty, but for longer horizons new ideas are needed.
The Southern Oscillation is measured by the pressure difference between the Tahitian port of Papeete and Darwin, Australia, which are about 7400 kilometers apart. When pressure in Tahiti is higher than in Darwin, La Niña occurs, bringing cooler water off the coast of South America.