## Demystifying Elliott Waves

Elliott waves can be recreated using the geometrical Time Triads.

It’s a rare chance that you have not heard about the Elliott Wave Theory. Named after Ralph N Elliott, the theory redefined Charles Dow’s theory of 1880′s where Dow talked about three legged bull market, and compared markets with ripples, waves and tides. Born on 28 July, 1871 Elliott was a genius just like 6 Nov, 1851 born Charles Henry Dow. They both had the ability to identify market patterns and hypothized a theory that stands firm till date. The Elliott forecast of a multi decade bull market made in 1935 at the bottom of the great depression can easily pass as the best financial forecast of all times. The work was generational in nature and was carried ahead by a string of elite practitioners Charles J Collins, A J Frost, Hamilton Bolton, Richard Russell and the famous Robert Prechter whose priceless contribution was instrumental in getting Elliott the much deserved attention.

Elliott wave hypothized that markets move in a 5-3 structure (Figure 1.), which created trends and counter trends. This structure happened at all time frames from the smallest tick data till century old data structure. Phelps Brown and Sheila V. Hopkins, (Oxford) estimated 1000 years of price history also has 5 wave structure. There are a total of 13 patterns which summarize all the price action and all technical analysis. Elliotticians have occasionally mentioned that technical analysis is a foot note in Elliott. If you read the historical work of Bolton, the accuracy is unprecedented. Prechter has written extensively illustrating how Elliott subsumes all conventional price patterns. Prechter claims it to be a science.

However despite the generational success and body of knowledge, there are heaps of criticisms against Elliott. First: Prove the science and mathematics (David R Aronson). Second: Standalone Elliott is fatal (Constance Brown). Third: Patterns are illusionary. Humans see what they want to see (Hersh Shefrin). Fourth: Markets are patterned but cannot be used to predict (Benoit Mandelbrot). Fifth: Price action is random (Nassim Taleb). Sixth: Markets are efficient (Eugene Fama). Seventh: Human beings like stories (Robert Shiller). There are many other issues concerning the practice of the technique. It’s a visual skill, which needs to be nurtured. There are not always perfect counts. Forecasting Time using Elliott is weak. A student has to go back in price history, which is always not easy, especially owing to the fact that society got used to high tech gadgets, computing power and Elliott wave counting softwares. We got used to fast solutions.

The criticism is not about just Elliott, it’s about everything technical. Head and shoulder pattern has come under much criticism from behaviorologists, statisticians and fundamentalists. Aronson goes ahead and carries a complete case called ‘head and shoulder’, objectification example. He systematically proves it bust. Aronson has been comprehensively harsh with Elliotticians and calls it a power of good story. This is what he says “The story gives Elliott analyst the same freedom and flexibility that allowed pre Copernican astronomers to explain all observed planetary movements even though their underlying theory of an earth centered universe was wrong”. First and foremost, Aronson’s labeling Prechter as a great story teller is highly critical. As Prechter has demonstrated enough accuracy over years and contributed to serious literature on markets and psychology. Second just because Elliotticians could not scientifically prove the mathematics does not make the Elliott wave a grand story, as we will explain ahead.

Figure 2.

Understanding the science in a theory takes time. Elliott did not use Fibonacci mathematics when he first hypothized the theory. At a suggestion he picked up books on Fibonacci and found it very compatible. In figure 2., you can see that Elliott can be counted mathematically in terms of exact numbers. The first subdivision is a cycle, one trend up and one trend down, which corresponds to Fibonacci numbers 1 and 1. The second subdivision when the uptrend divided into five waves and the down trend divides into three waves again correspond to Fibonacci numbers 5 and 3. As we go on subdividing we keep hitting numbers from Fibonacci sequence not only if we consider up trend and down trend separately, but even if we aggregate them.

How did Elliott miss it in 1934? Why is Elliott so countable? Does counting not make it mathematical? And why has nobody ever asked why Fibonacci and Elliott are so linked? What is the connection? Both change in prices, and Fibonacci numbers labeling the wave are exponential functions (Figure 3.). The magic of Elliott and Fibonacci lies in their exponential nature. There is such an extensive overlap of research historically that though Euler’s number ‘e’ (2.71828)) dates back to 1727, we have studied it in different forms, we never attempted to unify the forms. Starting from the marginal utility function, Pareto curve, Poisson distribution, fractals, are all linked with the exponential function just like Elliott.

Though Prechter mentioned that nothing much has been constructively added to Elliott since its creation, Tony Plummer’s seminal book was the first to demystify Elliott. The book first published in 1989 showcased a stylized pattern of time and suggested that time should nest and be fractalled. Plummer also went ahead and said that Elliott’s five wave structure was not the law of nature but the three wave structure of cycle was the real law of nature. This was a large thought, which we at Orpheus extended ahead into Time Triads, a hierarchy of triangles subdividing and multiplying by 3. Last feature we recreated the omnipresent head and shoulder formation (Plummer’s stylized pattern of time) by using Time Triads. Head and shoulder lost its mysticism as it could be created by a set of Euclidean triangles. The pattern was mathematical and fractalled. We created the pattern by assigning Cartesian coordinates to the units of Time Triads.

This is not the first time triangles have been used to create mathematical structures. Spidron is a field of triangles crumpled and twisted into a wavy crystalline seahorse’s tail. Then there are Koch Snowflakes which are created from inverted triangle or a V shaped structure. We have Pascal triangles. The oldest Pythagorean Theorem came from triangles.

Can time triads create Elliott wave structures and lay all the illusion of market patterns finally to rest and make market fractals a complete and validated science? This has been a quest for us since we coined the term Time Triads, Time Fractals 12 months back. Time Triads grow and decay exponentially with a factor of 3. We took two head and shoulder patterns created using Cartesian coordinates and did the same additive technique. We obtained a nine legged structure (Figure 4.) impulsing up and a nine legged structure moving lower. Elliott defines nine legs as an impulsive structure. Five wave structures are known to subdivide into nine waves.

Elliott wave talks about a stage in market when a corrective can drop 90%. The illustration (Figure 4.) is a complete cycle of a bull and bear market moving up and coming down in 9 legs. Another classic illustration of an Elliott structure is illustrated in Fig 5. Here we have an impulse followed by a sideways correction. This structure also has 9 legs moving up, and 9 legs moving sideways. There is no magic about 18 legs (9+9). There are 9 triangles making a larger triangle. And 9 triangles have a total of 18 sides. The magic of Elliott disappears. Now one may say what about the 13 patterns? We have assumed an idealized form of Time where larger Time does not influence smaller Time that is no translation. A computerized model where we account for translation can generate all the 13 patterns of Elliott.

There are no incomplete peaks in nature. What goes up invariably comes down, even if the uptrend is a century long. Growth and decay are parts of nature and markets. The reason Elliotticians could not prove the theory till now was owing to the fact that the big picture of time was missing. Time is bigger than generational knowledge. Time Triads just like Elliott can pinpoint where we are today and where we are headed tomorrow. There is no magic, it’s all geometry.

Where can I read about your postulation of the concept of Time Triads.

Sushil

The following feature was published in May 2008.

TIME TRIADS

http://timetriads.com/article/225