An explicit bi-variate stochastic model of the El Niño -Southern Oscillation system (ENSO) is built for the first time directly from observations of the Southern Oscillation Index (SOI) and sea surface temperature (SST) in the Niño region 3.4 (1876-2011). According to the resulting stochastic difference equation, the system remembers its past for two years, has the eigenfrequency 0.24 year -1 and the damping factors 0.5 and 0.05. Statistics of SST variations, including properties of El Niño and

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... La Niña, are also estimated through a Monte Carlo experiment. The time-domain model is used to describe ENSO in the frequency domain, including maximum entropy estimates of spectra, coherent spectra, coherence function, and frequency response function. The spectra are peaked at 0.22 year -1 ; the coherence increases from 0.6 at the lowest frequencies to over 0.9 between 0.18 year -1 and 0.33 year -1 exceeding 0.8 at all frequencies above 0.12 year -1 . This means that SST and SOI determine each other by up to 85% everywhere but at the lowest frequencies. The gain factor is peaked at 0.24 year -1 while the phase factor's magnitude is close to π everywhere. Therefore, the statistical predictability of the bi-variate ENSO time series does not improve much over the scalar case predictability.