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That's it, Tech. See, I knew someone was out there doing it, it is such an obvious idea. To gain access to the results we would need to be familiar with the literature, conference papers, abstracts, etc. It's a lot of work.
The trouble with high-order poly's is that they are well-behaved only within the original domain. They come in from infinity, oscillate about their zeroes, then zoom off to inifinity again. Typically the domain of interest is where they are oscillating. Outside that, they bomb.This is avoided by splines, which are piecewise continuous and fit smoothly together. But again, they only describe what we know, the historical period, and must be used with caution outside the domain, i.e., as a forecast tool.
Yes, math is (was) sort of behind all my studies. In meteorology we try to solve simultaneously a system of non-linear 2nd-order partial-differential equations derived from Newton's laws, laws of thermodynamics, ideal gas laws, etc., in three dimensions all in a rotating reference frame. It's a mess. Only by making a wholeseries of simplifying assumptions can they be solved analytically. Otherwise you have to use numerical methods which can only be approximately correct. Inevitably, the answer is a wave of some sort. And there is the problem of the data -- garbage in, garbage out.
But in the natural sciences we have the advantage of dealing with a rational system, one subject to natural law and nothing else. No amount of wishing can change the weather. In the market that is not the case. If enough people want something to happen, it will happen, in the market. Like say today every seller became a buyer; could happen. Or if some piece of bogus news causes every buyer to become a seller, suddenly. How do you model that?
Now we're getting into the realm of psychohistory, invented by Isaac Asimov in "Foundation". What we lack is a Hari Seldon! But...maybe I am talking to him right now? What are you working on, Tech?
Dave