Innovation (signal processing)

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An innovation in time series is the gap between what you observe at time t and what your model would have predicted using only past data. If the model is accurate, these gaps are uncorrelated and look like white noise. So the innovation series is what you get when you remove the predictable part of the measurements. The term was introduced by Hendrik Bode and Claude Shannon in 1950 during Wiener filter work (Kolmogorov had similar ideas earlier). The residual, by contrast, is the difference between the observed value and the updated value after including information up to time t.