新息

新息（英文：Innovation）係一隻差異值，嚟自變數喺時間t 嘅觀察值戥幫佢做嘅個最佳預測值之間做差，個預測值用到時間t 之前嘅可用訊息。若果預測方法工作得正常，係噉連續新息彼此之間冇相關，即構成白噪音嘅時間序列。即係話，從測量時間序列中獲得條新息時間序列，係通過「白化」或者潷丟啲預測得到嘅成分做到嘅。新息用喺時間序列分析（或者預測）當中，譬如統計學、訊號處理等啲領域當中；英文術語「Innovation」嘅使用源於 Hendrik Bode同Claude Shannon (1950) ^[1]喺佢哋對Wiener 濾波器問題嘅討論裏便，即管呢個概念早已着隱含喺Kolmogorov啲工作中。^[2]

相較之新息，殘差係個差異值，同樣嚟自變數喺時間 t 嘅觀測值，但戥佢做差嘅係個最佳更新狀態值，個狀態值基於直到（包括埋）時間 t 嘅可用訊息。

睇埋

考

↑ 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.

呢篇統計學文係楔位文。歡迎幫維基百科擴寫佢。

[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] 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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