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Strategies & Market Trends : Harmonic Trading with The Phoenix -- Ignore unavailable to you. Want to Upgrade?

To: Ramus who wrote (846)	7/7/2003 8:24:34 PM
From: the-phoenix	Read Replies (2) \| Respond to of 941

The idea of sixths is interesting, but maybe they aren't really sixths: .333 is gamma squared 1.33 is the cube root of pi .500, .667, 1.0, and 1.667 are from the fractional fibo series You know I'm funnin' ya now, right?

To: Ramus who wrote (846)	7/7/2003 8:51:40 PM
From: Haim R. Branisteanu	Read Replies (1) \| Respond to of 941

Walt I agree with your last paragraph. The reason that those numbers work sometimes is that many use them and believe in them. Unfortunate it is not as simple as many believe. The best example would be FX were most if not all participants are completely clue less and the use of TA levels are intensively used. The most amazing thing in FX are the bold predictions of the "experts" with complete disconnect from reality. Mostly amazing, are those daily predictions based on FIB numbers and EW Theory only to be violated again and again. One best example would be the recent gyration in the Sterling Euro and USD. The so called experts went from predicting 1.33 to 1 USD about 3 weeks ago to predict now 1.07 to 1 USD in EUR/USD pair. ....... all based on FIB numbers and ratios. Fundamentals such as trade imbalances, budget deficits, savings or real economic growth do not matter. Those issues are only used to justify FX moves after they already occured. IMHO because financial markets are mostly driven by sentiments and expectation the FIB number match some times or better said are used by market participants to achieve their goals.

To: Ramus who wrote (846)	7/9/2003 6:03:59 PM
From: Dan Duchardt	Read Replies (1) \| Respond to of 941

Nice post Walt. You have made some very interesting (to what our friend Phoenix calls MathHeads at least) observations about the Fib sequence and the related sequences. I was not familiar with the term "Fibonacci Cascade", but from your remarks about Phoenix's description of the ratios obtained by sectioning a line, I think what I was talking about goes a bit beyond that. All the ratios that result from the "Golden Section" are ratios of the higher elements of the Fib sequence, including the non-adjacent ones. All of these ratios are powers of PHI and phi. Hence, one can take roots of non-adjacent ratios that in some cases yield ratios of more closely spaced elements. Why not look at the roots of the primary ratios as a source of additional ratios of interest? The business of taking roots is, I believe, an extension of the Fibonacci Cascade and is apparently the origin of at least some of the additional ratios often considered important for TA. In particular the square roots of PHI and phi, and the square roots of those roots (fourth roots of PHI and phi) are among those ratios that magically appear in TA (1.272, .786, 1.128, .887) and they provide levels that nicely fill in the huge gaps between .618-1.000 and 1.000-1.618 that result from taking true Fib ratios (the ratio 1.000 is always justified IMHO, and clearly corresponds to the important TA levels of double top or double bottom. Another way to fill the gaps would be to extend the symmetry relationship inherent in the basic Fib ratios, .618 + .312 = 1. Why not create levels in the range .618 to 1 by subtracting any true smaller than .318 Fib ratio from 1, in effect turning the cascade divisions of an interval upside down? This yields numbers like .764, .854, .910. I don't recall ever seeing these numbers used for TA, but as with the roots it would be a logical extension. And if you construct any series based on sum of two as in Fibonacci you will construct an entirely different series but it's ratios will still converge to PHI and phi. Also, if you construct new series by sum of 3(Tribonacci) or 4(Quartonacci) etc these will converge to their own limits PHI' and phi'. This is some very interesting stuff I had not encountered before, so of course I had to take a closer look. You probably already know what I discovered, and I wont bore everyone with all the details, but it was interesting to note that for any "sum of two" sequence, the elements are of the form Aa + Bb, where a and b are the two initial numbers and A and B are coefficients that change from one element to the next. The coefficients A and B are, you guessed it, the Fibonacci numbers with B being the number that follows A in sequence. With a little algebra it is shown that the ratio of the higher adjacent elements in any "sum of two" sequence is the same as the ratio for the Fibonacci sequence. Similar results obtain for the "sum of N" sequences, with the coefficients being elements of the primary sequence for the first and the next higher element for the last of the N initial numbers. The "interior" coefficients each have their own sequence which is also a "sum of N" sequence that converges to the same ratio as the primary sequence. It follows that all such sequences of the same N converge to the same ratio. The adjacent ratios phi' for the "sum of N" sequences for N = 2, 3, 4, 5, and 10 are .618, .544, .519, .509, .50025. The limiting case for large N is clearly .5, which can easily be seen from any sequence formed by adding all previous elements. So if you don't like using the Fib ratio 1/2 to get .5, this limiting value of phi' is another way to get to that magic number. <ggg>