johnnyqpublic,
Let me back up. There is a theorem that a one or two dimensional random walk will visit any particular point infinitely many times if there is an infinite number of trials. The one dimensional case is called the Gamblers Ruin. So one dimensional games like this are poor betting games since your probability of returning to the origin (blowing out) is 100%. The two dimensional case has similar structure. However, in dimension n >=3, there is no certainty, and in fact the probability of returning to the origin decreases as the number of dimensions increases. In three dimensions however, the probability decreases to ~34%!!
This theory lends credence to taking action so that the number of degrees of freedom is at least three. Degree of freedom is the way mathematicians/scientists think of "dimension". Therefore, just from a mathematical point of view, trading at least three instruments against each other probably greatly reduces the odds of blowing out an account on the above argument. People that use a time series to predict the very time series are trading a random walk on a one dimensional line, no matter how many indicators you put on that time series!
NFV has way more than three inputs, and while I don't trade the other instruments against NFV (if I had a model for at least two of those that were predictive it would make sense and there are some inputs that have no trade-able counterpart), I still feel that I am not trading a one dimensional random walk.
To answer your last suggestion, of course inputs can become more or less "expressed". What you want is a theory of when. Some people use matching pursuits to model this sort of behavior. In the absence of a theory, the modeler has to shift his weightings accordingly. I have not done that because I feel it is intellectually dishonest. But if I had a mathematical way that did it for me, I would have no qualms about it. Me having to intervene and change the weightings manually may work, but then I won't be able to back test anything and all trading becomes live forward testing. Genetic weighting could work, but that seems too "curve fit" to me.
Maybe that is the real courage of the successful trader - not be afraid to change gears and realize that in today's markets, it is all forward live testing.
Right. That is not quite my purpose. You are trying to find predictive instruments you can trade against. I am building a model, and some of the inputs could be the number of sunspots at this given moment. Not quite the same thing...
Sure, that is not surprising to me. I am not a big fan of pairs unless the relationship is very strong. I find that when things go bad, you are left with two losing positions, not just one as in my case. You also incur twice the commissions and twice the slippage.
Most professional traders trade this way. Where we may disagree is in the instruments. For example, it could T-Bills against Eurodollars, or one end of the curve against another, or perhaps the SPY against the ES, or basis trading, etc, etc. This is more arbitrage than pairs. I am not a huge fan of pairs because it is a game that in my experience is extremely efficient these days. That doesn't mean it can't work.
Ok, here is the real reason I couldn't respond earlier, and where I am going to more or less agree with you, but perhaps for reasons that are not apparent at first.
Let me back up. There is a theorem that a one or two dimensional random walk will visit any particular point infinitely many times if there is an infinite number of trials. The one dimensional case is called the Gamblers Ruin. So one dimensional games like this are poor betting games since your probability of returning to the origin (blowing out) is 100%. The two dimensional case has similar structure. However, in dimension n >=3, there is no certainty, and in fact the probability of returning to the origin decreases as the number of dimensions increases. In three dimensions however, the probability decreases to ~34%!!
This theory lends credence to taking action so that the number of degrees of freedom is at least three. Degree of freedom is the way mathematicians/scientists think of "dimension". Therefore, just from a mathematical point of view, trading at least three instruments against each other probably greatly reduces the odds of blowing out an account on the above argument. People that use a time series to predict the very time series are trading a random walk on a one dimensional line, no matter how many indicators you put on that time series!
NFV has way more than three inputs, and while I don't trade the other instruments against NFV (if I had a model for at least two of those that were predictive it would make sense and there are some inputs that have no trade-able counterpart), I still feel that I am not trading a one dimensional random walk.
To answer your last suggestion, of course inputs can become more or less "expressed". What you want is a theory of when. Some people use matching pursuits to model this sort of behavior. In the absence of a theory, the modeler has to shift his weightings accordingly. I have not done that because I feel it is intellectually dishonest. But if I had a mathematical way that did it for me, I would have no qualms about it. Me having to intervene and change the weightings manually may work, but then I won't be able to back test anything and all trading becomes live forward testing. Genetic weighting could work, but that seems too "curve fit" to me.
Maybe that is the real courage of the successful trader - not be afraid to change gears and realize that in today's markets, it is all forward live testing.