The best line to draw that most traders will act on is one in the sand, where you say, "buy this index or we'll shoot." Alacrity will be their middle name. On the other hand, if you want to have a more subtle influence, you could put together a compendium of regressed factors from 20 or so commonly held (to be) indicatorial things, and combine them in a Fourier exercise of lofty and only slightly condescending authority, quoting Kondratieff and his wave as an aside. Better yet to use non linear regression before recombining. If it's too depressing, just forget it and fudge the curve to what everone wants to hear. Since every Guru since bin Adam has always been wrong 100% about ever stock and index, at least you will be in good company.
If you flipped a coing often enough you could simulate the behaviour of the exchange. With a properly weighted coin, which you experimentally construct by factor analysis, or other, you eventually find one that flips the same as the Dow moves. Since it is a physical coin, conundrum of having it obey long term laws of always favouring heads for 70 years at a time but only slightly, until for extended but briefer periods it favours tails, might be tough. It evidently has a bias that reverses every so often. It is hard to model randomly, don't you think?
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