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Harley's post raises a couple of thoughts. First, the number 0.618 is not a
Fibonacci number, but rather the number to which the ratio of successive
Fibonacci numbers converges as the series expands. As such, it is an
approximation by definition. Secondly, exchange quotes are quantized in
tick increments, which means the typical three decimal "Fib" ratio has more
significant digits than the prices allow one to use. As such, 0.625 or
0.600 are as good as 0.618 most of the time. The difference is even less
important if one is using time rather than price, as it is a rare occurrence
when (0.625 * some number of days) produces a result in days notably
different from 0.618 multiplied by the same value. It would seem a
significant variance wouldn't occur unless the time interval were minutes or
possibly even seconds. Whether Fib numbers or the ratios involving them are
useful in trading may be open to debate, but requiring the exact number
0.618 for market analysis is not necessary or practical.
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Harley Meyer wrote:
<Let me throw a fly in the ointment of Fibonacci here. I would say that
<most folks would not argue with me if we said that a fib retracement of
0.618 is approximately 2/3 and .382 is approximately 1/3. Likewise
0.61803999 is approximately 0.618. So do I place my trade or support
line at the fib number or at the other fractions. Since they are very
close.
The point that I am trying to make is that in mathematics everything is
defined to have a very specific meaning. For example 0, 1, 1, 3, 5, 8,
... is defined to be the fibonacci sequence. 0, 2, 4, 6, 8, ... is NOT
the fibonacci sequence, by definition. The "NOT" that I am using is the
'logical' not that turns a true statement into a false statement and
vice versa.
(I hope you can see where this is going by now.)
So if the retracement was actually 0.61803999999999999... which isn't a
fibonacci number then the retracement isn't fibonacci. Some ratios that
are observed in nature that are fibonacci are exact, not approximations.
Hopefully this takes us back to trading using Fibonacci techniques is
more of a social construct than being one with nature. Let alone by
definition it isn't even Fibonacci, since an approximation of a
Fibonacci number is Not a fibonacci number.
<Just something to think about.
<
<Harley
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