Any STABLE distribution has a logic (set of trading rules) that has positive expectations. For example: if the markets were truly Gaussian then the short option strangle positioned at 2 STD would be 100% guarantee winning strategy providing there is a stop loss at 1 STD. You can verify it for yourself. However, the markets, of course, are not Gaussian. So what would be the measure that would determine the "Skew" in its distribution? You are right, one of them is arcsine law, another is the "Mean Deviation Ratio" = squareroot(2n/pi) where n is the number of steps that the market makes on average to reach a certain price change. One can use it to determine the exact skew and build the algorithm to exploit it. Interesting, isn't it?
It seems to me that the definition of random needs to be nailed down. If someone said I was trading a random market but there is flocking I would say that market is not random. If you can beat the flock and then get the flock out with a profit that is not random. Not in my definition of random. It might be random at your level of analysis - but not mine. I am beginning to wonder if random is a substitute for incomplete analysis. Essentially the flocks movement may be random to the migration tracker, but it would not be to a bird in the back of the pack. Markets might be random to a set of tools attempting to forecast a daily price change and at the same time there might be times where the market is quite organized to a an experienced scalper with a tic chart.
It cannot be more clear than this: http://en.wikipedia.org/wiki/Stochastic_process From WikiPedia: ...."Familiar examples of processes modeled as stochastic time series include stock market and exchange rate fluctuations, signals such as speech, audio and video, medical data such as a patient's EKG, EEG, blood pressure or temperature, and random movement such as Brownian motion or random walks. Examples of random fields include static images, random terrain (landscapes), or composition variations of an heterogeneous material..."
Personally, I would agree with your 'strict' definition of non-random, jem. Since we know that various human behavioral biases are manifested in the mkt, they are not random. Therefore, as you suggest, we can presume that good traders are able to systematically take advantage of these biases to consistently outperform. But that brings me to something that always puzzled me. Specifically, what does the conclusion above actually have to do with technical analysis? Why would you rely on inconclusive indicators that may or may not be a proxy to the specific biases you're trying to take advantage of? To me that's simply intellectually deficient. Basically, instead of doing the difficult analysis to isolate the phenomena they're interested in taking advantage of people prefer to just draw squiggles on their charts. It's true that some of these random squiggle methods do work as expected by providing a proxy to biases (the 'resistance' at round numbers comes to mind). Still, when you're trading, wouldn't you actually want to know exactly what your decisions are based on? BTW, apologies to MAESTRO et al, if I am digressing...
You are not digressing; you are, actually spot on! By asking yourself these kind of questions one can eventually enlighten him/her self by slowly coming to the right conclusions. As to me, THERE ARE NO COMPELING REASONS FOR TA TO WORK AT ALL, however there are million occurrences that make the TA tools spontaneously work. That reinforces our blindness towards the true nature of things.
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Just out of curiosity, I have run a random walk simulation exercise, where I simulate 5000 steps, starting at level 1000 (let's pretend this is the S&P not so long ago ^^), a fixed (for now) step size of 0.5, and a random distribution of step directions as follows: 40% up, 40% down, 20% flat. kind of wild guess of an index trapped in a trading range or something... I have added an SMA on the chart, for the heck of it And here's the result of 1 run of simulation: Oh sh*t! I think I see a couple of nice trending "corridors" with precise S and R lines, then a break of the S trend line followed with a so classic re-test... not to mention on the right side of the chart this quasi perfect double-bottom - better yet, an Adam&Eve type of double bottom, the TA people here will appreciate the nuance... ^^ So what shall I deduce from such an experiment...? :eek: I'm afraid I'm not going to enjoy the answer...