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Separately, here's a curve ball.. Maybe fibs are useful to the reader as a heuristic. A move with a 68% retracement may give rise to a certain intuitive feel as to what may happen next.
I agree the notion that the market "has" to move a certain way (fib or otherwise) is complete BS, but perhaps the right brain uses fibs as a compression algo to store memory of past price action.
Perhaps the market doesn't obey fibs but our brains use them to store memories so we think the market does. Our wetware did evolve in an environment chock full of fibs after all. Using fibs in memory formation would be an efficient way to internally represent the world around us.
I find this comment very pertinent for this discussion. Right brain is non-verbal and intuitive. Maybe a fib user is a person that uses his right brain more than his left hemisphere which is more verbal and analytical for reading the markets.
When you say "a lot", do you mean they happen more than random? Wouldn't one then be able to just hunt for 50% retracements and expect to be able to trade them profitably?
All the technical indicators use either the price or the volume to compute information. Fibonacci indicators use neither price not volume, so it is strictly not a technical indicator, hence it is cannot provide an entry or exit points like MACD, RSI etc.
Fibonacci tools can be used for visually representation of possible pullback or trend extremes. In my experience, trends usually go to about 100% Fib extension (ie, about same range of prior trend). Retracements are that useful beause there are too many levels too close to each other (23.6%, 38.3%, 50%, 61.8% ... ).
Experiment with them. If you find them helpful use them. No need to do elaborate studies on this subject, IMO.