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 â 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_{t-1}, y_{t-2}, y_{t-3}, \ldots, u_{t}, u_{t-1}, u_{t-2}, u_{t-3}, \ldots) + \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 Îµ 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. ==external links== * open-source implementation of the narx model using neural networks
Nonlinear_time_series_analysis Stochastic_processes Time_series_models