Neural network and algorithm(s), predicting future outcome from past

Question

I was working on a algorithm, where I am given some input and I am given output for them, and given the output for 3 months (give or take) I need a way to find/calculate what might be the future output.
Now, this problem given can be related to stock exchange, we are given certaing constraints and certain outcomes, and we need to find the next.
I stumbled upon neural network stock market prediction, you can Google it, or you can read about it here, here and here.

To get started at making the algorithm, I couldn't figure out what should be the structure of layers.
The given constraint are:

• The output would always be integer.
• The output would always be between 1 and 100.
• There is no exact input for say, just like stock market, we just know that the stock price would fluctuate btw 1 and 100, so we might (or not?) consider this as the only input.
• We have record for last 3 months (or more).

Now, my first question is, how many nodes do I take for input?

The output is just one, fine. But as I said, should I take 100 nodes for input layer (given that the stock price would always be integer and would always be btw 1 and 100?)

What about hidden layer? How many nodes there? Say, if I take 100 nodes there too, I don't think that would train the network much, because what I think is that for each input we need to take into account all previous input also.

Say, we are calulating output for 1st day of 4th month, we should have 90 nodes in hidden/middle layer (imagining each month is 30 days for simplicity). Now there are two cases

• Our prediction was correct and outcome was same as we predicted.
• Our prediction failed, and the outcome was different than what we predicted.

Whatever the case be, now when we are calculating the output for 2nd day of 4th month, we need not only those 90 input(s) but also that last result (and not the prediction, be it the same!) too, so we now have 91 nodes in our middle/hidden layer.

And so on, it would keep increasing the number of nodes each day, AFAICT.

So, my other question is how do I define/set the number of nodes in hidden/middle layer if its dynamically changing.

My last question is, is there any other particular algorithm out there (for this kinda thing/stuff) that I am not aware of? That I should be using instead of messing around with this neural networking stuff?

Lastly, is there anything, that I might be missing that might cause me (rather the algo I am making) to predict the output, I mean any caveats, or anything that might make it go wrong that I might be missing?

Answer 1

There is much to tell as an answer to your question. In fact, your question addresses the problem of time series forecasting in general, and neural networks application for this task. I'm writing here only several most important keys, but after reading this you should possibly dig into Google's results for the query time series prediction neural network. There is a lot of works where the principles are covered in details. A variety of software implementations (with source codes) do also exist (here is just one of examples with codes in c++).

1) I must say that the problem is 99% about data preprocessing and choosing correct input/output factors, and only 1% about concrete instrument to use, whether neural networks or something other. Just as a side note, neural networks can internally implement most of other data analysis methods. For example, you can use neural network for Principal Component Analysis (PCA) which is closely related to SVD, mentioned in another answer.

2) It's very rare that input/output values are strictly fit a specific region. Real life data can be considered as unbounded in absolute values (even if its changes seem producing a channel, it can be broken down just in a moment), but neural network can operate in a stable conditions only. This is why the data is normally converted into increments first (by calculating deltas between i-th point and i-1, or taking log from their ratio). I suggest you do it with your data anyway, though you declare it's inside [0, 100] region. If you don't do it, neural network will most likely degenerate to a so called naive predictor which produce a forecast with each next value equal to previous.

The data then is normalized into [0, 1] or [-1, +1]. The second is appropriate for the case of time series prediction where +1 denotes move up, and -1 - move down. Use hypertanh activation function for neurons in your net.

3) You should feed NN with an input data obtained from a sliding window of dates. For example, if you have a data for a year and every point is a day, you should choose the size of window - say, a month - and slide it day by day, from the past to the future. The day just at the right bound of the window is the target output for NN. This is a very simple approach (there are much more complicated), I mention it just because you ask how to handle data which does continuously arrive. The answer is - you don't need to change/enlarge your NN every day. Just use a constant structure with a fixed window size and "forget" (do not provide to the NN) the oldest point. It's important that you do not treat all the data you have as a single input, but divide it into many small vectors and train NN on them, so the net can generalize data and find regularity.

4) The size of sliding window is your NN input size. The output size is 1. You should play with hidden layer size to find better performance. Start with a value which somethat between input and output, for example sqrt(in*out).

According to lastest researches, Recurrent Neural Networks seem operating better for tasks of time series forecasting.