NARX (Nonlinear autoregressive with external input) neural network学习

最新推荐文章于 2024-06-27 00:03:06 发布

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最新推荐文章于 2024-06-27 00:03:06 发布

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NARX（非线性自回归外部输入模型）是一种用于时间序列建模的非线性自回归模型，考虑了外部输入的影响。这种模型常用于预测和描述自然界、经济学等领域的时间序列过程。在MATLAB中，可以使用'narxnet'命令创建NARX网络，并通过'closeloop'和'preparets'函数进行数据预处理和模型训练。NARX网络适用于处理包含非线性和反馈机制的时间序列预测问题。

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先看Wikipedia中的简要介绍：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 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 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 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