QuoteDislikedSo the conclusion is that a "random" data set offers predictability by way of mean reversion, but an "unpredictable" data set does not. Terminology!
Hehe, what you're talking about is a random distribution or a chaotic data set. For instance rolling a dice with a constantly changing number of sides.
This would occur whenever the number of possibilities is unknown or whenever there are dependencies between trials that we can't map. Which fits the market pretty well, you may have 20% win/loss in one set of trials or one pair, 50% in another, 80% in another, and anything in between for all the rest. Keep in mind tho you can still run a 2nd order on the probabilities and determine a min/max/mean and stdevs on the probabilities themselves. That means unless the set is completely chaotic there are still patterns in the mist and ways we can recognize optimum (or not) strategies. I have never seen a purely chaotic data set, and odds are I won't live to (entropic death of the universe? lol). It also means that a perfectly optimum strategy that works one minute may suddenly stop working another, and start working again later on.
That's why I said, and still claim, that profitability is far less about finding a high win/loss ratio and more about managing risk. As you said, profitability is win/loss times an R value, with both being inverse properties. But the R value is a factor of return on risk, and return can't be evaluated until after the trade is done. Meaning that over a large enough time frame, as the random distributions of the market play out (and blast away any attempts at quantifying them), the most consistent factor we can control is our risk exposure.
QuoteDislikedI think that's a reasonable assumption. If you'd started trading your USDJPY crossover system last year (assuming a similar optimization [16/18] was available then), the equity curve shows that you'd now be in profit. Same if you started 2 years ago. Same 3 years ago. And so on. So why not the upcoming year also? At each point on your equity curve, the future was every bit as unknown as is the case currently.
I think it's an assumption that's made, and the market has bore it out over time, but I see no reason why this must be so. In general, many of the same basic inefficiencies still exist, but the way to exploit them has changed over time.
QuoteDislikedthe optimal parameters change as you reduce the size of the data set. the fact that the 18/16 for USDJPY did well over all years was remarkable. in fact, it is the only one size fits all cross i've found (although i haven't spent much time exploring other pairs.)
Nod. The classical problem of infinite variance. But does it matter? If it provides a good enough entry over a large enough time frame and a large enough set of pairs, then even if it varies a bit you should still be fine. When doing entry studies it's usually best to only try and predict a fixed number of bars after the entry, usually only the next one.
Test example:
For every cross, determine how often the next bar is bull and how often it is bear, and how often your cross accurately predicts it. What are the odds for each pair? What are the minimum odds in any given pair (over time), what are the maximum, etc. Do you notice any trend bias in those statistics? etc, etc. Now increase the sample to 2 bars... 3 bars, 5 bars, etc.
What you'll probably find is that your cross is accurately determining the trend direction, but is useless on days that go the opposite direction. I've found a number of strategies to help minimize that downside.
), your discussion on randomness are not less enjoyable than the Wimbledon's finals 
Tdion, thanks for allowing them to stretch their brain muscles on this thread.
