Abstract
An index consisting of the difference of normalized sea level pressure departures between Tahiti and Darwin is used to represent the Southern Oscillation (SO) fluctuations. Using a time-domain approach, autoregressive-moving average (ARMA) progress are applied to model and predict this Southern Oscillation Index (SOI) on a monthly and seasonal basis. The ARMA process which is chosen to fit the monthly SOI expresses the index for the current month as a function of both the SOI one month and seven (or nine) mouths ago, as well as the current and previous month's random error. A purely automotive (AR) process is identified as representative of the seasonal SO fluctuations, with the SOI for the current season being derived from the index for the immediate past three seasons and a single random disturbance term for the current season. To allow for the phase locking of the SOI with the annual cycle, ARMA processes with seasonally varying coefficients are also considered.
As one example of how these models could be used, seasonal SO variations have been forecast. When SOI observations from 1935 through the summer of 1983 are employed, the seasonal model indicates forecast of positive SOI from fall 1983 through fall 1984. Forecasts based only on SOI observations from 1935 through spring 1982 show a low predictive skill for the SOI values from summer 1982 through winter 1984, whereas one-season-ahead forecasts starting with summer 1982 agree reasonably well with the actual SOI observations. These examples help illustrate the degree to which the future behavior of the SOI is predictable on the basis of its past history alone.
