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)[1] in their discussion of the Wiener filter problem, although the notion was already implicit in the work of Kolmogorov.[2]
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.
^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 ISBN0-7803-0434-9
^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.
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innovation, signal, processing, time, series, analysis, forecasting, conducted, statistics, signal, processing, many, other, fields, innovation, difference, between, observed, value, variable, time, optimal, forecast, that, value, based, information, available. 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 1 in their discussion of the Wiener filter problem although the notion was already implicit in the work of Kolmogorov 2 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 editKalman filter Filtering problem stochastic processes Errors and residuals in statistics Innovation butterflyReferences edit 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 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 nbsp This statistics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Innovation signal processing amp oldid 1213447945, wikipedia, wiki, book, books, library,
