No, a curve-fit is a curve-fit. With a 0-100 integer (not floating point) range on one parameter, combined with 3 more you get 100 million possible combinations. That's a lot of room for a curve-fit with only 4 parameters. Even using 3 possible values for each will give you a curve-fit. The idea is to have other statistics that backs up a possible fact that what is found is a fundamental market rule, and not a curve-fit. How that's done is a different matter.
If you are not using integer values in your example (like you said 15.something%) then the ranges 0-100 or 0-100000 really don't matter since floating point value is just that, an almost unlimited number of numerical representations in 8 bytes of information.
In other words, it doesn't matter if there are constraints. It might just happen that a value of a parameter at 22.22222 % produces a great looking model, but 22.22223% doesn't. That means it's just a "magic number" that's there due to luck, not real substance (same thing alexandermerwe mentioned).
No, a curve-fit is a curve-fit. With a 0-100 integer (not floating point) range on one parameter, combined with 3 more you get 100 million possible combinations. That's a lot of room for a curve-fit with only 4 parameters. Even using 3 possible values for each will give you a curve-fit. The idea is to have other statistics that backs up a possible fact that what is found is a fundamental market rule, and not a curve-fit. How that's done is a different matter.
If you are not using integer values in your example (like you said 15.something%) then the ranges 0-100 or 0-100000 really don't matter since floating point value is just that, an almost unlimited number of numerical representations in 8 bytes of information.
In other words, it doesn't matter if there are constraints. It might just happen that a value of a parameter at 22.22222 % produces a great looking model, but 22.22223% doesn't. That means it's just a "magic number" that's there due to luck, not real substance (same thing alexandermerwe mentioned).
OK, let me phrase the issue slightly differently, if you don't mind. If I have a one parameter model that can take a value from 0% to 100% (e.g., the parameter measures the odds of some other thing happening) and the outcomes when that parameter value is from 0% to 50% are negative (on average) and from 51% to 100% are positive (on average), is that likely to be a "fundamental market rule" or is that curve-fitting and it is likely to be the case in the future that even those scenarios where the parameter value is from 51% to 100% will be negative, thus making the model's overall value negative? I realize that perhaps the rule could be more finely cut and the likely outcome might be negative all the way up to 50.4999999999% and the positive outcomes actually start at 50.5%, but let's just keep this example a bit more simple than that. So, I'm not selecting a single value for the parameter, but I am defining a set of values within the parameter's allowable range which I would know from my historical data would lead to a negative outcome on average, meaning that now I have myself a viable way of filtering out trades as undesirable as well as a way of identifying positive expectancy trades, based on the one parameter.
Or, at least, is it less likely to be curve fitting than saying that 50 is the ideal parameter value for a moving average which could range from 1 to almost any number? Because while you can identify a range in the example above, you can't say that any moving average in a range of 0 to 50 will work as your parameter value, it has to be one number to drive the model. It's either 50 or it's something else, whether that be 49, 51, whatever.
This is the distinction I am trying to articulate, now that I think about it more.
... So, I'm not selecting a single value for the parameter, but I am defining a set of values within the parameter's allowable range which I would know from my historical data would lead to a negative outcome on average, meaning that now I have myself a viable way of filtering out trades as undesirable as well as a way of identifying positive expectancy trades, based on the one parameter.
...
I think bounded and un-bounded are equivalent and that the same rules apply. You can often transform a bounded variable to an unbounded one and visa versa.
For instance, for a moving average you can look at the period from 1 to infinity. If you in stead look at frequency (which is equivalent) you're looking at the range of 1 to 1/infi=0, i.e. the bounded interval of ]0;1].
I think you ignore the fact that any indicator can be forced to be range-constrained between some fixed numbers.
But when you are optimizing, why would you take an indicator reading on, to stick with the moving average example, and force it to be a moving average between 10 and 20 periods? You would, at some point, pick the best possible value for the number of periods. If 17 gives you the best results, you would only use 17. I've not heard of anyone using a moving average strategy which says to enter if any moving average from the 48 to the 52 crosses over any moving average from the 196 to the 204, for example. Sure, some people try to get cute and use the 49 over 199 as the "golden cross" and I get that, but it is still a single value for each parameter in the optimization. I suppose you could have multiple instances of a MA crossover strategy, each with a different set of optimal values, though.
It still seems like that is different from optimizing to find a range of values which can serve as action triggers, as in the example which I used of entering if the odds of something are above 50% and not entering if they are below 50%. There, whether the odds are 51% or 95%, you take the same action because the expected value of that action is positive. If the odds are 49% or 0%, you don't take action because the expected value is negative.
Admittedly, this is a little different from the original contrast I laid out, but this is really what I was getting at.
