Archive for the ‘Fractals’ category

Benner, Pareto and the structure of time

Benner was the first one to illustrate time hierarchy and Pareto showcased hierarchy in everything. Could they have connected the idea in 1900 before the Pareto curve?

Benner’s Prophecies - Future up and down in prices was written in 1875. A keen technician will sooner or later hit the fascinating time geometry of the Benner cycle. Samuel Benner was a prosperous farmer wiped out financially by the 1873 panic. He turned to wheat farming in Ohio and took up the statistical study of price movements as a hobby to find, if possible, the answers to the recurring ups and downs in business. He noted that highs of the business tend to follow a repeating 8-9-10 yearly pattern. With respect to economic low points, he noted two series of time sequences indicating that recessions (bad times) and depressions (panics) tend to alternate.

I updated the Benner cycles and they suggest a top in 2010, a slowdown and low in 2011, a cycle high again till 2019 and then depression in 2021.

Time Triads, Time Fractals, Time Arbitrage, Performance Cycles are terms coined by Orpheus Research. Time Triads is our weekly market letter. The report covers various aspects on TIME patterns, TIME forecast, alternative research, emerging markets, behavioral finance, market fractals, econohistory, econostatistics, time cyclicality, investment psychology, socioeconomics, pop cultural trends, macro economics, interest rates, derivatives, money management, Intermarket trends etc.

This article is written for Association of Technical Market Analysts


Life and coastlines

Some problems span multi generations, Benoit Mandelbrot solved one such problem and earned himself a well deserving place in history, as the father of fractals.  Many of these mathematical structures and their descriptions go back to classical mathematics and mathematicians of the past like Cantor, Peano, Hilbert, Koch, Sierpinski, Julia, Hausdorff, but it was Mandelbrot who extended the early topology. Fractals solve the problem of how to organize complicated structure in an efficient way. Of course this was not what Peano and Hilbert were interested in almost 100 years ago. It was only after Mandelbrot’s work that the omnipresence of fractals became apparent.

Mandelbrot was a visionary in his ability to connect mathematics and patterns. He too like many other great thinkers worked on ideas of aggregation, simplification, order, efficiency rules, cyclicality in errors, interconnectedness of nature through geometrical structures. Mandelbrot illustrated that very simple formulas can generate objects that exhibit an extraordinary wealth of structure. His work encompasses mathematics, physics, economics and diverse other fields of physical and social sciences, music and art. He died on 14 Oct at the age of 85 after suffering from pancreatic cancer.

Time Triads, Time Fractals, Time Arbitrage, Performance Cycles are terms coined by Orpheus Research. Time Triads is our weekly market letter. The report covers various aspects on TIME patterns, TIME forecast, alternative research, emerging markets, behavioral finance, market fractals, econohistory, econostatistics, time cyclicality, investment psychology, socioeconomics, pop cultural trends, macro economics, interest rates, derivatives, money management, Intermarket trends etc.

This article is written for Alrroya


Can Time Triads create the head and shoulder fractals?

Time Triads recreating head and shoulder fractals is a step closer to rewriting the Elliott Wave Theory.

We have talked about head and shoulder on prior occasions. We have also mentioned that time is a head and shoulder. The time pattern was first illustrated by Tony Plummer in his book. Plummer mentioned that a stylized pattern of time was a good example of fractal geometry.

Tony Plummer’s Stylized Time Pattern

He did not give a formal pattern proof of creation for the stylized pattern. Where did the stylized pattern come from? How could it be seen across time frames? And how was it fractalled?

Orpheus Introduces TIME TRIADS

Here we have taken the Orpheus Time Triad unit and reworked on it to create the stylized pattern Plummer first illustrated in his book. The stylized pattern looks like a head and shoulder. Time Fractals, Time Triads, Time Arbitrage, Econohistory, Performance Cycles are terms coined by the author in Jan 2009.

The idealized time triad structure is made of equilateral triangles. There are three equilateral triangles, making a larger triangle and so on. Time subdivides in three and multiplies in three. What is with the formation? First and foremost: Head and Shoulder are three peaks, a large peak centered around two smaller peaks. Head and shoulder pattern is the time triad i.e. three triangular peaks. Did you ever think why a day has four prices, the open, the high, the low and the close? We just take it as standard. Ok! it does look logical to have the O-H-L-C, but the interesting part is how this classification divides the trading session into three parts. There is a part with the open and high, high and low, low and close. The three triangles of head and shoulders are there. Market literature is full of pattern ideas from human anatomy. It’s not that just chance that we find similar patterns in markets like we find in human anatomy. We find head and shoulders in markets just like we see it in human body is because time touches anatomy, the same way it transforms price.

Nature unlike markets doesn’t just move in the first Cartesian quadrant with positive x and y axis values. Nature moves in all dimensions, in free space. Fabian Helge von Koch (1870 – 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described. The Koch snowflake (or Koch star) is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled “On a continuous curve without tangents, constructible from elementary geometry”. The Koch curve starts from a Triangle and in the second iteration divides each side of the triangle into a head and shoulder form. The iterations are repeated and this creates the Koch curve. Koch curve is a zooming head and shoulder bombarding in your eyes like a moving spatial star field.

The Head and shoulder pattern can even rewrite the Dow Theory and even explain the Elliott Theory. Elliotticians are known to famously quote that there are few rules in markets, mainly the EWT (Elliott Wave Theory) works on guidelines. The only two rules in the long standing Elliott Theory is that the 3rd wave is never the shortest of the three impulsing waves 1, 3, 5. What Elliott unknowingly said was that the three up legs in a five legged market structure have a bump or a head, simply putting the middle part of a market fractal is larger than the other two. The 3rd is never the shortest because of the Head and Shoulder. The pattern of time rules the Elliott fractal. There is another rule of Elliott that the 2 wave does not make a new low below the low of 1. The head and shoulder pattern of time also makes higher lows and not lower lows. A higher degree of time does indeed make more significant lows than its small degree counterparts.

So what did we do with the Time triads? We gave the smallest triangle a size of 1 unit (X). 3 units made a larger triangle (3X) and nine units made the larger triangle (9X). At all times these unit lengths are adding or subtracting. Assuming there is no translation. That is largest time is not effecting the smaller time. Putting simply the bear market is the same in potential and scope as the bull market, the markets will behave ideally, losing all the gains it made, a classic cycle.

Doing an aggregation of three degrees viz. X, 3X and 9X, we reached the Head and shoulder pattern. And as we added a higher degree head and shoulder fractals started to form.

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