Fibonacci Sequence

R. N. Elliott's analysis of the mathematical properties of waves and patterns eventually led him to conclude that "The Fibonacci Summation Series is the basis of The Wave Principle".Numbers from the Fibonacci sequence(1,2,3,5,8,13,21,34,55....) surface repeatedly in Elliott wave structures, including motive waves (1, 3, 5), a single full cycle (8 waves), and the completed motive (89 waves) and corrective (55 waves) patterns. Elliott developed his market model before he realized that it reflects the Fibonacci sequence. "When I discovered The Wave Principle action of market trends, I had never heard of either the Fibonacci Series or the Pythagorean Diagram".

The Fibonacci sequence is also closely connected to the Golden ratio (1.618). Practitioners commonly use this ratio and related ratios to establish support and resistance levels for market waves, namely the price points which help define the parameters of a trend.

Finance professor Roy Batchelor and researcher Richard Ramyar, a former Director of the United Kingdom Society of Technical Analysts and formerly Global Head of Research at Lipper and Thomson Reuters Wealth Management, studied whether Fibonacci ratios appear non-randomly in the stock market, as Elliott's model predicts. The researchers said the "idea that prices retrace to a Fibonacci ratio or round fraction of the previous trend clearly lacks any scientific rationale". They also said "there is no significant difference between the frequencies with which price and time ratios occur in cycles in the Dow Jones Industrial Average, and frequencies which we would expect to occur at random in such a time series".

Robert Prechter replied to the Batchelor–Ramyar study, saying that it "does not challenge the validity of any aspect of the Wave Principle...it supports wave theorists' observations," and that because the authors had examined ratios between prices achieved in filtered trends rather than Elliott waves, "their method does not address actual claims by wave theorists". The Socionomics Institute also reviewed data in the Batchelor–Ramyar study, and said these data show "Fibonacci ratios do occur more often in the stock market than would be expected in a random environment".

Extracted from the same relationship between Elliott Waves and Fibbonacci ratio, a 78.6% retracement level is identified as a best place for buying or selling (in continuation to the larger trend) as it increases the risk to reward ratio up to 1:3.

It has been suggested that Fibonacci relationships are not the only irrational number based relationships evident in waves.