More Than One Step in the Future

In the previous analysis, we used the NN to predict only one future step. However, it is possible to use our model to predict more than one step in the future. There are two ways of doing that. The first way is to train a NN having $m$ outputs (number of future steps) and the same past inputs as our model (time, day, windows). This model is very naive and its performance is very bad. We propose a more sophisticated way to predict the future steps of the traffic by proceeding as follows. The same NN model as we described in Section 9.2 is to be used to predict $F(T+1)$ as before. The same trained NN is then to be used to predict $F(T+2)$ by setting $F(T-i)=F(T-i+1),\, n\geq i\geq 0, \, F_y(T-j)=F_y(T-j+1),\,y \geq j\geq 0, \mbox{ and } F_w(T-k)=F_w(T-k+1),\,w \geq k \geq 0$. We can continue to predict more than two steps in the future in the same way. We used our model to predict the second step in the future for the whole next two weeks from the past values using the same trained NN described in Section 9.3.4, and obtained a MSE of 0.006. We show in Figure 9.8, the difference between the actual and the predicted traffic for the complete next two weeks for the second step. As we can see the performance of our model is good enough to predict even more than one step in the future.

Figure 9.8: Predicting 2nd step ahead: the difference between the actual traffic and the predicted one for the complete next two weeks, including the spikes.