**4. NARX model architecture**

NARX model defines the output as a function of its inputs and its past outputs as described in the following equation [8],

$$\mathbf{y(t) = f\left[\mathbf{y(t-1), y(t-2), \dots, y(t-d\_y); u(t-1), u(t-2), \dots, u(t-d\_u)\right]} \tag{1}$$

**Figure 2.** NARX model standard architecture.

**Figure 3.** Example NARX model standard architecture *(3 inputs, 1 hidden layer, and 1 output).*

Where u represents the exogenous data and y are the NARX model outputs. du and dy present respectively delays order of inputs u and outputs y. **Figure 2** presents the NARX model standard architecture.

For example, the NARX architecture of a neural network composed of three inputs, one output and six neurons in its hidden layer is presented as shown in the **Figure 3**.
