Growth and decay have always been associated with nature, assets, life but rarely with time. From April 2008 - March 2009 we have been publishing ideas linked with time cyclicality and fractals and starting Mar 2009 we have expanded the idea of time coining ideas like time triads, time fractals, time arbitrage, and performance cycles. We have illustrated long-short pair trading cases between India - China, Czech - Poland, BSEOIL v/s Sensex, Gold v/s Oil, Nikkei v/s India, Soya v/s Shanghai and many other single asset ideas.

We talked about the work of a few Nobel Prize winners, work of various experts, authors and thinkers over the last 250 years (and more). Euclid, Leonardo Fibonacci, Adam Smith, Thomas Malthus, Maynard Keynes, Vilfredo Pareto, Pierre Francois Verhulst, Karl Marx, Charles Dow, Karl Lamprecht, J M Draper, George Cantor, Ralph N. Elliott, Kinglsey Zipf, Joseph Kitchin, Clement Juglar, William Berry, Daniel Kahneman, Benoit Mandelbrot, Robert Shiller, Hersh Shefrin, Martin Pring, John Murphy, Theodore Modis, Bill Meridian, William Strauss and Neil Howe, Tony Plummer, Eugene Stanley, Robert Prechter, etc. We covered a lot of market research literature to illustrate a few simple ideas. First: Time cyclicality was a reality. Second: Over a few hundred years, research (mathematical, historical, scientific, market related, psychological) overlapped. Third: Time was the pulse or the soul of everything.

The theory of Time

The third idea is and will be contested as it simplifies many lifetimes of work. It challenges Mandelbrot's Chaos theory assumption and fractalness of nature. Time and price can't be fractalled at the same time so it consequently proves that Elliott wave theory of price is actually a theory of time. The idea of time fractal also moots that efficient and inefficient market theories (behavioral and others) are two faces of the same coin, the real risk comes from time translation and Pareto principle is because of time triads.

To demonstrate my case, I shall take global assets, isolate time periodicities and illustrate time decay. If time decays similarly across respective assets over various periods of studies then there is indeed something about ‘Time’ that can't be ignored. The following assets were taken: Gold, Dow, Oil, Indian Sensex, Indian CNXIT futures (technology Index Futures), Japanese Nikkei, Romanian Blue chip BET and Euro-Dollar currency pair. I took all the available history from my Thomson Reuters 3000 Xtra terminal. Some data periods were from 1955, a few from 1965 and the majority from the 1990's.

The experimentation

What did I do with this data? The price was de-trended first. What was left was an oscillator on an x-axis with calendar dates. These calendar dates were nothing but time cycles with time periodicities in days, weeks, months, hours, etc. The time periodicities were sorted on a descending basis in the number of days and plotted them. The result is the following charts (illustration).

All the charts not only looked similar but decayed in an exponential way. Students of Pareto principle, mathematics, econophysics, and Mandelbrot fractals will say "so what is surprising here? This is a clear expression of the power law." Look again at the charts, there is no price in the charts. It is just time decay. Above that, the similarity of the charts is irrespective of the asset and the period of study.

What does it mean?

This means that time grows and decays exponentially and because of which asset prices seem to grow and decay exponentially in a power law basis. It also means that either time is exponential or price is. Both cannot grow and decay at the same time exponentially. This also proves that all the focus on studying news, information, prices, psychology, sentiment, and mathematical order are indirect ways to study time.

If you look at the charts and cases further you will see that most assets when plotted on a daily basis had an average periodicity of 15-20 days, when plotted on a weekly basis had an average periodicity of 66-77 days, when plotted on a monthly basis had an average periodicity near 400 days.

Now, that it all looks coincidental, the data of all the days was plotted, from 23 April 1997 since I first wrote in Business Standard. Guess what? Over the respective publishing period of near 13 years, the time difference between my features also decayed exponentially. In conclusion, the power law 80-20 rule that has been omnipresent in nature, markets, and societies turns out to be also present in time.

This aspect proves that time is not a linear moribund constant but a living pulsating variable which gives life to everything else. If global traded assets and a time series of a decade-long personal event create similar patterns, we cannot keep living the illusion that time has no pattern and mathematics. The idea of randomness falls on its face when mathematics and order get associated with time.

Time fractals are the reason why opportunities - crisis, war - peace, creation - destruction will recur irrespective of any human effort. The exponential growth and decay of time suggest that we have a lot of unlearning to do. And before we do that, we should give time cyclists there due place in the history of research, at least on par with psychologists, technicians, historians, and mathematicians.