Editing Elliott wave principle (section)

==Fibonacci relationships==
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".<ref name=Masterworks/> Numbers from the [[Fibonacci number|Fibonacci sequence]] surface repeatedly in Elliott wave structures, including motive waves (1,&nbsp;3,&nbsp;5), a single full cycle (8&nbsp;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".<ref name=Masterworks/>

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.<ref>Alex Douglas, "Fibonacci: The man & the markets," Standard & Poor's Economic Research Paper, February 20, 2001, pp. 8–10. [http://www.analistademercado.com.br/Fibonacci01.pdf PDF document here] {{Webarchive|url=https://web.archive.org/web/20070226070759/http://www.analistademercado.com.br/Fibonacci01.pdf |date=2007-02-26 }}</ref>  See [[Fibonacci retracement]].

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".<ref>Roy Batchelor and Richard Ramyar, "Magic numbers in the Dow," 25th International Symposium on Forecasting, 2005, p. 13, 31. [http://www.cass.city.ac.uk/media/stories/resources/Magic_Numbers_in_the_Dow.pdf PDF document here] {{webarchive |url=https://web.archive.org/web/20090918053822/http://www.cass.city.ac.uk/media/stories/resources/Magic_Numbers_in_the_Dow.pdf |date=2009-09-18 }}</ref>