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Help wanted on on statistics / testing approach for prediction
I will hint that important rules to bear in mind are that (1) correlation does not imply causation, and (2) description and prescription. Historically, most daily deaths occur on the days I wear black underwear. That's nice to know and very descriptive, but it is probably not a prescriptive relationship.
If you think of it in this way, you don't need formal mathematics to gain an intuition for many statistical problems that you are encountering.
I was hoping there might be a better methodology/approach and there would be others who understand the problem better. This is why I asked for help and started the thread.
Your reply is too scholarly for me to understand:
"each of the random variables is itself a member of some non-stationary stochastic process."
1. I do not believe the variable are independent. As stated they are all based on the same data series -specifically EOD data for the ES. I would expect that they are non-independent.
2. I do understand that correlation is not causation, but I believe I am a long way from there and it is like sinking the boat before I can even find it! One has to start somewhere. I'm still in the water.
Your reply does not seem to offer an alternative approach.
I am stuck a bit with the "classifications" of the EOD closes. Is each day assigned one such class or are multiple classes assigned to each day?
So is the following something like the language?
- A = Close Up from previous day
- B = Close Up from previous day by large amount
- C = Close Down from Previous day
- D = Close Down from Previous day by Large amount
Or do they classes reach back further?
- A = Closed up 1 day in a row
- B = Closed up 2 days in a row
- C = Closed up 3 days in a row
I am starting to get your approach. I think Rapid Miner may help as I think you have created a class of "things":
A, B, C, D, E,... U
What I think might help here is to develop a Fitness function. So create a function that does something like what you have stated, but I think of it this way:
Fitness=k1*A+k2*B+...+Kx*U
You can then use a generic algorithm to "search" this function to maximize the fitness function. k1, k2 ... kx are likely one of 3 values -1, 0, +1 (NOT, absent, Present).
This is the approach I would likely take to solve this as you have stated you have ~20 possible input combinations which leads to a very large search space.