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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Nonlinear autoregressive exogenous model ： ウィキペディア英語版 Nonlinear autoregressive exogenous model In time series modeling, a nonlinear autoregressive exogenous model (NARX) is a nonlinear autoregressive model which has exogenous inputs. This means that the model relates the current value of a time series where one would like to explain or predict to both: * past values of the same series; and * current and past values of the driving (exogenous) series — that is, of the externally determined series that influences the series of interest. In addition, the model contains: * an "error" term which relates to the fact that knowledge of the other terms will not enable the current value of the time series to be predicted exactly. Such a model can be stated algebraically as : $y\_t\; =\; F(y\_,\; y\_,\; y\_,\; \backslash ldots,\; u\_,\; u\_,\; u\_,\; u\_,\; \backslash ldots)\; +\; \backslash varepsilon\_t$ Here ''y'' is the variable of interest, and ''u'' is the externally determined variable. In this scheme, information about ''u'' helps predict ''y'', as do previous values of ''y'' itself. Here ''ε'' is the error term (sometimes called noise). For example, ''y'' may be air temperature at noon, and ''u'' may be the day of the year (day-number within year). The function ''F'' is some nonlinear function, such as a polynomial. ''F'' can be a neural network, a wavelet network, a sigmoid network and so on. To test for non-linearity in a time series, the BDS test (Brock-Dechert-Scheinkman test) developed for econometrics can be used. == References == * S. A. Billings. "Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains, Wiley, ISBN 978-1-1199-4359-4, 2013. * I.J. Leontaritis and S.A. Billings. "Input-output parametric models for non-linear systems. Part I: deterministic non-linear systems". ''Int'l J of Control'' 41:303-328, 1985. * I.J. Leontaritis and S.A. Billings. "Input-output parametric models for non-linear systems. Part II: stochastic non-linear systems". ''Int'l J of Control'' 41:329-344, 1985. * O. Nelles. "Nonlinear System Identification". Springer Berlin, ISBN 3-540-67369-5, 2000. * W.A. Brock, J.A. Scheinkman, W.D. Dechert and B. LeBaron. "A Test for Independence based on the Correlation Dimension". ''Econometric Reviews'' 15:197-235, 1996. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Nonlinear autoregressive exogenous model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.