imported>GhostInTheMachine: Changing short description from "Difference between the observed value of a variable at a certain time, and the forecast of that value based on information available prior to that time" to "Difference of forecasted and actual values"

2024-04-30T17:28:17Z

Changing short description from "Difference between the observed value of a variable at a certain time, and the forecast of that value based on information available prior to that time" to "Difference of forecasted and actual values"

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{{Short description|Difference of forecasted and actual values}}
In [[time series analysis]] (or forecasting) — as conducted in [[statistics]], [[signal processing]], and many other fields — the '''innovation''' is the difference between the observed value of a variable at time ''t'' and 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 noise]] time 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 Bode]] and [[Claude Shannon]] (1950)<ref>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}}</ref> in their discussion of the [[Wiener filter]] problem, although the notion was already implicit in the work of [[Kolmogorov]].<ref>Mitter, S. K. (1982). Nonlinear filtering of diffusion processes a guided tour. In ''Advances in Filtering and Optimal Stochastic Control'' (pp. 256-266). Springer, Berlin, Heidelberg.</ref>

In contrast, the residual is the difference between the observed value of a variable at time ''t'' and the optimal updated state of that value based on information available till (including) time  ''t''.

==See also==

* [[Kalman filter]]
* [[Filtering problem (stochastic processes)]]
* [[Errors and residuals in statistics]]
* [[Innovation butterfly]]

==References==

{{reflist}}

{{DEFAULTSORT:Innovation (Signal Processing)}}
[[Category:Statistical signal processing]]

{{statistics-stub}}

Innovation (signal processing) - Revision history

imported>GhostInTheMachine: Changing short description from "Difference between the observed value of a variable at a certain time, and the forecast of that value based on information available prior to that time" to "Difference of forecasted and actual values"