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	~~Andrew Berryhill~~ is ~~what his wife enjoys~~ to ~~contact him~~ and ~~he totally digs~~ that ~~title~~. ~~She~~ is ~~truly fond~~ of ~~caving but she doesn~~'~~t have~~ the ~~time recently~~. ~~Alaska~~ is the ~~only place I~~'~~ve been residing in but now I~~'~~m contemplating other choices~~. He is ~~an info officer~~.~~<br><br>My page; tarot card readings~~ ([~~http~~:~~//www~~.~~sivuland~~.~~biz/pods/show/great~~-~~hobby~~-~~advice~~-to-~~assist~~-~~get~~-~~you~~-~~going www~~.~~sivuland~~.~~biz~~])		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 which 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

			: <math> y_t = F(y_{t-1}, y_{t-2}, y_{t-3}, \ldots, u_{t}, u_{t-1}, u_{t-2}, u_{t-3}, \ldots) + \varepsilon_t </math>

			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 [[errors and residuals in statistics\|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.

			==External links==
			* [http://sourceforge.net/projects/narxsim Open-source implementation of the NARX model using neural networks]

			[[Category:Stochastic processes]]
			[[Category:Time series models]]
			[[Category:Nonlinear time series analysis]]

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Andrew Berryhill is what his wife enjoys to contact him and he totally digs that title. She is truly fond of caving but she doesn't have the time recently. Alaska is the only place I've been residing in but now I'm contemplating other choices. He is an info officer.<br><br>My page; tarot card readings ([http://www.sivuland.biz/pods/show/great-hobby-advice-to-assist-get-you-going www.sivuland.biz])

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en>David Eppstein: /* See also */ Dini criterion

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