Innovation (signal processing )

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In time series analysis(or forecasting) — as conducted in statistics, signal processing, and many other fields — the innovationis the difference between the observed value of a variable at time tand the optimal forecast of that value based on information available prior to time t .If the forecasting method is working correctly successive innovations are uncorrelated with each other, i.e., constitute a white noisetime series .Thus it can be said that the innovation time series is obtained from the measurement time series by a process of 'whitening', or removing the predictable component .The use of the term innovation in the sense described here is due to Hendrik Bodeand Claude Shannon(1950) ^[1] in their discussion of the Wiener filterproblem, although the notion was already implicit in the work of Kolmogorov. ^[2]

See also

• Kalman filter
• Filtering problem (stochastic processes)
• Errors and residuals in statistics
• Innovation butterfly

References

1. C.E.Shannon and H.Bode: A simplified derivation of linear least square smoothing and prediction theory, Proc .IRE, vol .38, pp. 417-425, 1950, reprinted as Chapter 51 in The Collected Papers of Claude Shannon, IEEE Press, 1993 ISBN 0-7803-0434-9
2. S.K.Mitter: Nonlinear filtering of diffusion processes, Springer (1982)