Benoit Mandelbrot, the father of fractal geometry saw fractals everywhere. He might just have missed seeing them on TIME.

**FLUCTUATIONS AND TIME ACCORDING TO MANDELBROT**

A fluctuation is a pulse, a change, amplitude. In a heartbeat a fluctuation signifies life. Researchers have spent decades researching fluctuations in an attempt to understand markets. Few like Mandelbrot have even gone ahead and defined nature by proving that the fluctuations are mathematical, fractalled. The father of fractal geometry illustrated the vastness of the idea, but he failed to extend the idea to time.

According to him though TIME does not run in a straight line, it changes according to price and stretches and shrinks like a balloon rubber. It speeds up and slows down. The 1993 Wolf Prize winner (most prestigious award after the Nobel Prize) focused all his mathematics on price and not on TIME. The seriousness of his work suggests that either TIME was not important enough to be featured in his lifelong work or he did not consider TIME to have a mathematical fluctuation or in words an organic life.

**NOT THE ONLY ONE TO IGNORE**

He was not the only one to ignore it, history of research starting Euclid never thought about TIME as a living pulsating system. Behaviorologists are far away from quantifying the subject and are more busy highlighting behavior errors rather than looking at something non-descript, as TIME. Barring a few, majority of behavioral finance researchers might consider fractal nature of emotions as ridiculous idea, leave aside fractal nature of time. Isn’t it strange, we have so many organic systems and entities built in and around time viz. the society, a market, nature, humans and the only thing, which we assume could not have life was TIME itself. The few, who thought, researched and wrote about time as a pulse, a cycle never made many decibels (fluctuation). Their ideas remain buried and unprinted, out of circulation, outside mainstream economics, more peripheral than the other struggling subject of pattern and fractal watchers, Technical Analysis.

**WHAT HAPPENED? **

How did Mandelbrot miss it? Mathematicians claim themselves to be purists working without assumptions. Mandelbrot cracks a joke on economists, as the ones who assume in his book, ‘The (Mis) behavior of markets’, missing a key and rather significant thought. The slip-up was monumental.

Equality, mean, price independence has been the corner stone of modern finance. Mandelbrot challenges the modern finance techniques and calls them as “foolhardy underestimation of risk of ruin”. The ‘Bell Curve’ has an equal portion of standard deviations on each side. Tests proved that in real situations the ‘Bell Curve’ fails miserably. Prices cluster and do not take a bell shape form. Mandelbrot also says that prices are not predictable or controllable, therefore seeing nature through probabilities theory is tough. “If the physical world is so uncertain, how much uncertain must be the world of money”. “Fractal geometries multifractals begin with the realization that mean is not golden”. It also goes ahead and challenges the work of Louis Bachelier, Harry Markowitz, William Sharpe and Eugene Fama. Till it was modern finance it was fine, but it seems Mandelbrot assumed a similar equality for TIME, which was static and perfect rather than proportional or fractalled as he saw it in price.

**WHAT ABOUT PROPORTION?**

The power law was more about proportion than mean or equality. The law applies to negative and positive price movements, leaves room for big price changes far away from mean. If everything in nature was proportional (language, income, markets, nature, etc.), based on the Vilfredo Pareto 80-20 statistical distribution and the unchallenged ZIPF law, then why was TIME harshly judged on equality. Cyclical periodicity written and researched for more than 200 years did not exhibit perfect regularity but an average periodicity. Samuel Benner demonstrated the cyclicality of 16-18-20 and 8-9-10 repetitive year cycles. William Strauss and Neil Howe presented a strong case for an intergenerational, 85- to 99-year cycle. Brian Berry pointed to the presence of a generation-length, 25- to 35-year, cycle. Clement Juglar reported a medium term, seven- to 11-year, cycle. Joseph Kitchen reported a short-term, three- to five-year, business cycle. Business cycles were some observation, which according to Mandelbrot occurred and disappeared. And strangely all the above cycles had a mathematical proportion X, X/3, X/9, X/27. Despite such research Mandelbrot did not mention TIME. For him TIME was not alive, not proportional, and had nothing to do with fluctuations, which were just meant for price and nature.

**THE PARTIAL PATTERN**

There were further partial omissions. Mandelbrot gives a large weightage to pictures in identifying fluctuations. “Assault on normal with pictures not numbers”, “pictures are undervalued in science”, “Financial prices has memory and today influences tomorrow”, “Different kind of prices, different degrees of memory”. “Fractal geometry is about spotting repeating patterns”. “Pictures say more than words” His idea of “Price dependence” also gives credit to history”. However, this past to future linkage, cyclicality was just limited to identifying the fluctuation patterns.

This was partial acceptable of pattern recognition on one side and on the other he said there was no predictable pattern. Price had the memory of 1929, time had no memory. On one side he said, “The wigglies (fluctuations) looked the same in different times” and on the other he trashes all ‘Head and Shoulder’ watching. “My mathematical models can generate charts that purely by the operation of random process appear to trend and cycle”. A similar exercise of computer generated charts were put in Hersh Shefrin’s book ‘Greed and Fear’. The aim was to highlight that conventional chartists can’t differentiate original from fake. This was a very crude way to judge the pattern recognition skill. Mandelbrot says “pattern watching at times can be correct”, “everybody knows about support points”, “technical analysis is financial astrology”, and “pattern watching is for neophytes”.

**THE PREDICTABILITY CONUNDRUM AND THE QUESTION OF WHEN?**

Though pattern watchers are pulled down by both psychologist and mathematicians, it’s only the pattern watchers who are left to predict and claim that forecasting works. Despite all the mathematics and psychology understanding, both behavioral finance and fractal geometry schools say that predictability is an illusion. Mandelbrot even goes ahead and says that ‘Fluctuations’ are predictable not what is between them.

With all this behavioral and mathematics understanding, the only lesson fractal geometry teaches us is how to avoid losing money. But you can only avoid losing money if you invest first. Whom should the investor go to, if he needs an investing advice? Behavioral finance says advisors don’t know, just diversify, buy the losers, sell the winners and save. The majority will herd again and the bubbles will come again, as a repeating fluctuation and cyclical pattern unfolds. Both the pattern bashers never address ‘WHEN’? The sentiment indicators that are supposed to give some indication are also junked by psychologists. So we have these grand theories, which tell us how to avoid risk and losses, but they don’t tell us ‘WHEN’ to invest? The question of TIME is not their business.

If all this was not enough, Mandelbrot says that “markets are not chaotic unlike the chaos theory it espouses and one should not attempt to TIME”. Robert Shiller used larger market extremes (fluctuations) in 1980 to challenge efficient theorists and Robert Prechter rolled out Elliott fractal work (similar to Mandelbrot’s multi fractal) in a systematic way, applying it for predictive work since 1970. Both Mandelbrot and Shiller suggest predictability is tough and an illusion respectively.

**TIME FRACTALS VS. PRICE FRACTALS**

In his 1999 article, “A multifractal walk down wall street”, Mandelbrot used a 3 wave pattern, the first and last being in the direction of the general trend, the middle against the general trend to illustrate how market fractalled by subdividing in similar forms. A picture of his example from the article is illustrated (left hand side).

He focused on the price and not the TIME. This is the reason why price fractals and TIME fractals seem disconnected. We redrew Mandelbrot’s multifractals from a TIME cycle (up leg and down leg) rather than** **from a price trend (up leg - down leg - up leg) perspective (right hand side). TIME fractals break down into X, X/3, X/9, X/27 and further on just like the documented economic cycles. A triangle breaking down into three smaller triangles and so on.

**X- AXIS AND Y AXIS**So now either TIME is fractalled or price and nature is. It’s a simple mathematical idea that both X and Y axis cannot have a fractalled pattern at the same time. The Y axis contains all of Mandelbrot’s nature symmetry and beauty while the X axis just has TIME. One of the ideas is wrong, either TIME is not fractalled or only TIME is fractalled giving everything a beauty and a form. Just to prove our case we starting looking for TIME TRIADS (time fractals) on a ratio line (remember long India, short china). We were not surprised. The triads were there too. TIME was indeed a THREE, working independent of the Y axis. Draw a rate of change on a price or a price ratio or on any time series, you will see them.

Tony Plummer in his book ‘Forecasting financial markets’ does give reference to time cycles as a triad of patterns, but does not extend the work to fractals.

**CONCLUSION AND CHAOS**

TIME fractals change the way we look at nature. It brings order in the disorder of the Chaos Theory. Butterfly effect suddenly starts to lose its mystery. The sensitivity dependence the Chaos theory talks about is owing to the genetic code of time, which is always different as there is an infinite TIME above and below us. We may have some TIME till we find the next theory of everything, but till then start watching the fluctuation.

Download the latest TIME TRIADS report timetriads2505091

Author: Mukul PAL | Date: 22 May 2009 | Comments (6)

Tags: Berry, cyclicality, fluctuations, fractal geometry, Kitchin, multifractals, power law, price dependence, Strauss, time fractals, Time Triads, Zipf

Categories: Time Triads

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