Functional auto-regressive forecasting of ENSO climatic variations

Many variations such as the annual cycle of sea surface temperatures can be considered to be smooth functions and are appropriately described using methods from functional data analysis. This study de-nes a class of Functional Auto-Regressive (FAR) models which can be used as robust predictors for making forecasts of entire smooth functions in the future. The methods are illustrated and compared with pointwise predictors such as SARIMA by applying them to forecasting the entire annual cycle of climatological El Ni~ no-Southern Oscillation (ENSO) time series one year ahead. Forecasts for the period 1987-1996 suggest that the FAR functional predictors show some promising skill, whereas traditional scalar SARIMA forecasts perform poorly.