Yes I think empirical testing is the only answer. Basically you'd program your charting software to buy each of the different gap formations separately over say a ten year period and see which of them closed the gap in 'x' days and what % gain/loss with gap+1 day, 2 day 3 day etc.. Wouldn't be a complex programming task.
It surprises me how many books on charting, even the well known ones, don't test there theories at all. They say "buy when stochastic oversold and MMA's crossed on higher volume - wow what a system!!"...then you go home and and actually program that and test it over multiple years and multiple markets and it fails miserably. In fact I've looked through almost all of the books on charting at some point or other and don't think I've ever come across a proper backtest or walkforward test. The real deal on charting is not found in books but in research publications and peer review finance journals.
It's a bit like saying "garlic cures the common cold". You have to do a placebo-controlled randomised trial...not one but many ....to actually validate that statement, otherwise it has no meaning and is likely to be completely false.
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Yes I think empirical testing is the only answer. Basically...
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