If one redraws Mandelbrot's multifractals from a time cycle (The up leg and the down leg) rather than from a price trend (The up leg - The down leg - The up leg) perspective, the same multifractals emerge out as time fractals Fig 3. This is one reason why the debate regarding who saw it first, Elliott or Mandelbrot is inappropriate when one realizes that time fractals are more proportionate than price fractals. Time is an underlying variable, which is tougher to relate compared to price. Human beings as a society can relate more to what they can see and feel. This is the reason why price fractals and time fractals seem disconnected. Mandelbrot multifractals focused on the price and not the time. A picture of his example from the article “A Multifractal Walk Down Wall Street” is illustrated in Fig 2. Mandelbrot used a 3 wave pattern, the first and last being in the direction of the general trend, the middle against the general trend. A multifractal is formed by a curve pattern being repeated at smaller and smaller time scales. The term fractal, as Mandelbrot defined it, refers to a curve in which distinct parts are smaller scales of the whole curve. 1 Economic cycles ruled by a factor of 3.ģ: If it is assumed that time fractals can be isolated, similar cycle periodicities can be witnessed and isolated in intermarket ratio lines, which are independent of price.Ĥ: The cycle periodicity was tabulated and tested for power law distributions.ĥ: The K/9 time fractal periodicities on intermarket ratio line are tested in the long-short strategy. The cycle characteristics were kept in mind before isolating the K factor. This means that if we isolate the Kitchin (K) cycle of 40- 44 months, which is widely witnessed, we could identify lower hierarchies i.e. This hence is not a chance event, but owing to time fractal nature. William Strauss and Neil Howe, Brian Berry, Clement Juglar, and Joseph Kitchin, which are connected by 3. They are also more proportionate than price fractals.Ģ: The above mathematical proportion X, X/3, X/9, X/27, etc can be seen in the economic group of cycles (Fig. This suggests that time cycles are fractals that showcase self-similarity with a factor of 3. This study further connects its findings with the existing research on various economic cycles finally extending the proof to a long-short Intermarket strategy on an asset pair.ġ: Cycles underlie fractals and Mandelbrot's multifractals can be redrawn from a cycle perspective. These were a few reasons why time fractals remained unproven. Even few Elliott wave practitioners have admitted the limitation of the Elliott Wave structure as being sharper on form than on time. Patterns are understood either conventionally or as Elliott wave fractals. Cycles are not conventionally believed to be patterned. The continued prosperity after the 1980s was a reason why time fractals did not get researchers' attention, unlike price fractal which was actively studied and researched.
#A MULTIFRACTAL WALK DOWN WALL STREET SERIES#
Long-term time series are difficult to obtain and many emerging markets have seen stock market trading activity only started a decade back. Testing cycle periodicity needs large historical data. The power law in prices is a subject of extended study, but there has been no research attempt made to prove power law in time cycle periodicities. Power law is seen across nature and in diverse social trends. The case is validated by illustrating power-law curves in time cycle periodicities. The enclosed research reworks the Mandelbrot Multifractal from a time cycle rather than trend perspective to prove that time fractal is more proportionate than the price fractal and is the real law of nature, which drives everything in nature. In February 1999, Benoit Mandelbrot submitted an article to Scientific American called ”A Multifractal Walk down Wall Street.” In the article, he discussed how fractal geometry can be used to model the stock market curves.
#A MULTIFRACTAL WALK DOWN WALL STREET PROFESSIONAL#
The book brought fractals into the mainstream of professional and popular mathematics. In 1975 Benoit B Mandelbrot coined the term fractal and in 1982 published his ideas in ‘The Fractal Geometry of Nature'. Elliott wrote the wave principle in 1938. A lot has changed since then but challenging Mandelbrot remains a Herculean task.
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