Why the faith in ANN?

17Sep10

An intuitive explanation.
Look at this chart that shows the average daily %return distribution from 2004 to 2005 for the day of the week. As usual, on the X axis, we show the day of the week. 1 means Monday, 5 represents Friday.

Average daily %return distribution from 2004 to 2005.

In this 2 years period, the next day %returns are bullish on Monday and Friday. That is clear. It is bearish on Tuesday and Thursday. But what can we say on Wednesday? One tempted to say that is bullish, but is it really? I wouldn’t bet on the bullishness of the Wednesday. Why? Because that is most probably just a randomness in the training samples. I would deem Wednesday to be bearish.

So, why to have faith in ANN?

1. ANN should be better than linear regression.
Try to regress a linear line to this distribution. Good luck. 🙂
You can, but it will be a line that will be bullish on every day (and the slope increasing). One can say that forming the problem in this way (we crammed the inputs (1..5) into one 1 dimensional vector) is not ideal for linear regression. That is true, but put it off for a while.

2. ANN should be better than k-NN
What a k-Nearest Neighbour like algorithm would do with this distribution? It would most probably find k training samples, each of them would be Wednesday (if k is small). So, its aggregate estimation would give most probably a positive %gain.

What would an ANN do with this distribution? It should match a parabolic shape to it. That function would be smooth. I would smooth out the response for Wednesday and would give a bearish signal for Wednesday. It would smooth out the randomness inherent in the training samples. And we like this behaviour.

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