I'm on my little holiday so I'm hoping to post a few things for a week. For starters, I'll just throw a question... How do (I didn't write "would") you develop a profitable trading system/model (infrastructure) on a (pseudo-)random data? When I mean instrastructure I mean by AI, ML, Self-generating models, automated/non-automated system development paradigm and whole bunch of other stuff. Random meaning... both real market data, data generated based on market character (like Brownian of some market distrib.) or CS pseudo-random like Quantum and other simpler ones... Hopefully this becomes fun... and hope this is more interactive than a one way street.
Few Random Data 101 stuff... http://www.zoology.ubc.ca/~rikblok/lib/blok00b.pdf http://www.columbia.edu/~mh2078/MCS04/MCS_framework_FEegs.pdf http://homepage.mac.com/j.norstad/finance/finplan.pdf
One way you could (I didn't write "do") approach the problem, is the methodology embodied in this commercial product: http://www.stratasearch.com/ You could use the commercial software itself. Or you could extract the ideas from the commercial product and embed them into other software of your own choosing, perhaps LIM or Matlab or R or NumPy.
From an intuitive standpoint you can think of the arcsine law as "the longer you stay in a position, the more you can make". I'm not being flippant, and this is a very important concept. re: random data, what do you mean by "develop a profitable system?" Random entries can become profitable via exits that themselves could be entries; you simply end up keeping the entries that "agree" with your model. So is your question really "how do I decide when/where/how to exit?" There are a lot of reasons to think exits are more important than entries, so this is a worthwhile exercise.
Ok, let's start with a fun probability game. Just one assumption though: - The data has a known normal-like distribution. So, here's the process: 1. Create a random number generator that pulls a "random" number using the distribution we have. Let's call this number "R". 2. If the current value of the of the random stream, call it "C" is greater than R, then the current value is likely to be "high" with a probability of 0.66. 3. Vice versa for "low" values. How do we create a trading rule out of this? Can we assume binary outcomes? Mike