The bell curve issue is a basis for some of our analytics so it seems like this is a good place to give our point of view. This is in regard to Aphie's first post.
What if things are happening on different timeframes? What if 90% of the movement of the stock could be explained by the movement that is obvious in your graph, a bell curve. But what if there were stronger, slower currents also affecting the price? For example, imagine that the stock price moves up by an average of $0.01 per day for 3 months, then goes down an average of $0.01 per day for 1 month. These movements could never be explained by your original model. In fact, you couldn't even see these movements in your model because they would be too small compared to the noise. But if you did the same thing with 1 week movements instead of 5 minute minutes, the trend would become perfectly clear.
These slower, stronger currents might also look something like a bell curve. Lets create an example. Look at picture #1. Series1, the blue line, is a standard bell curve. Series2, the magenta line, is another bell curve with a standard deviation that is 3 times as big as the standard deviation of the original. A better model would probably use a standard deviation of 10-1000 times this size, and a 1% - 0.1% contribution, but for this example I chose numbers that are easy to see on the graph. Series3 is 90% of series1 and 10% of series2. Series3 is probably pretty close to what you observed. If you didn't see it next to the other examples, series3 would look like a bell curve, but the tails are higher than they should be.
Picture #2 zooms in on the tails. Here you can see that the new curve, Series3, is significantly different than the real bell curve, Series1. In is segment, the real curve varies from about 12,500 times the value of the bell curve to 150,000,000 times the value of the bell curve. All of the actual values are small, but they can really add up over time. There is also a difference in the middle of the bell curve, but that is a much smaller percentage.
Now, an alternative way to look at the same thing. Let's say that you only trade end of day. (This works in any timeframe, but let's keep this example consistent.) Everything you saw in your original experiment is noise; you can't trade it and it gets in the way of what you're looking for. You are looking for the $0.01 average change per day described above; this trend is consistent enough to make money. So, how do you separate the trend from the noise? Your experiment was the first step. You are calibrating the noise. You can now say which moves can be explained completely by noise. Moves which are too large or too consistent to be represented by the noise are worth a closer look. These represent the real trend. These moves are what you see when your tails deviate from the bell curve.
See
http://www.trade-ideas.com/DOSA/ for more information.
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Thanks