# The Time Decay

The exponential decay of time proves that all the focus on studying news, information, prices, psychology and mathematical order are indirect ways to study time.

Growth and decay has always been associated with nature, assets, life but rarely with time. From Apr 08 – Mar 09 we have been publishing ideas linked with time cyclicality and fractals and starting Mar 09 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 vs. Sensex, Gold vs. Oil, Nikkei vs. India, Soya vs. 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, Brian 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 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. I took the following assets, 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 majority from 1990’s.

What did I do with this data? I detrended the price. I was left with 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. I sorted the time periodicities on a descending basis in numbers of days and plotted them. I got 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 power law.” Look again at the charts, there is no price in the charts. It’s just time decay. Above that, the similarity of the charts is irrespective of the asset and the period of study.

What does this 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 can’t 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 an indirect way to study time durations.

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, I plotted the data of all the days from 23 Apr 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 globally 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 their due place in the history of research, at least at par with psychologists, technicians, historians and mathematicians.