Neural network training

We have time series, i.e., a variable x changing in time x_t (t=1,2,...) and we would like to predict the value of x in time t+h.

The prediction of time series using neural network consists of teaching the net the history of the variable in a selected limited time and applying the taught information to the future. Data from past are provided to the inputs of neural network and we expect data from future from the outputs of the network (see the figure 2).

As we can see, the teaching with teacher is involved. For more exact prediction, additional information can be added for teaching and prediction, for example in the form of interventional variables (intervention indicators) - see the figure 3. However, more information does not always mean better prediction; sometimes it can make the process of teaching and predicting worse. It is always necessary to select really relevant information, if it is available.

Various types of neural networks can be used for prediction, such as backpropagation, ART, Marks network and others. In the rest of this text we will focus on backpropagation.

Figure 2 - teaching of time series without interventional variables. The points in
graph represent time series obtained by sampling of continuous data.

Time series with interventional variables

Figure 3 - Teaching of time series with intervention indicator