Multi Step Prediction Neural Networks

Question

I have been working with the matlab neural network toolkit. Here I am using the NARX network. I have a dataset consisting of prices of an object as well as the quantity of the object purchased over a period of time. Essential this network does one step prediction which is defined mathematically as follows:

y(t)= f (y(t −1),y(t −2),...,y(t −ny),x(t −1),x(t −2),...,x(t −nx))

Here y(t) is the price at time t and x is the amount. So the input features I am using are price and amount and the target is the price at time t+1. Suppose I have 100 records of such transactions and each transaction consists of the price and the amount.Then essentially my neural network can predict the price of the 101st transaction. This works fine for one step predictions. However, if i want to do multiple step predictions, so say i want to predict 10 transactions ahead(110th transaction), then I assume that i do a one step prediction of the price and then feed this back into the neural network. I keep doing this until I reach the 110th prediction. However, in this scenario, after i predict the 101st price , I can feed this price into the neural network to predict the 102nd price, however, I do not know the amount of the object at the 101st transaction. How do I go about this ? I was thinking about setting my targets to be the prices of transactions that are 10 transactions ahead of the current one, so that when I predict the 101st transaction, I am essentially predicting the price of the 110th transaction. Is this a viable solution or am i going about this in a completely wrong manner. Thanks in advance for any help

Answer 1

I guess you can use a separate neural network to do time series prediction for x in order to produce x(t+1) up to x(t+10) and then use these values to feed another ANN to predict y(t).

Answer 2

Similar to what kostas said, once you have the predicted 101 price, you can use all your data to predict the 101 amount, then use that to predict the 102 price, then use the 102 price to predict the 102 amount, etc. However, this compounds any error in your predictions for each variable. To mitigate that, you can add several other features, like a tapering discount on past values or a measure of error to use in the prediction (search temporal difference learning for similar ideas in the reinforcement learning realm).