Archive for the ‘Time Decay’ category

Time decay in Fed funds rate change

Interest rates are supposed to be a central banker domain. To suggest that time proportion and pattern acts here too is no short of economic blasphemy. We took the data for all Fed Funds rate changes since 1994, tabulated them and sorted the changes in time between the rate cuts. We got the classic time decay function yet again. Is this coincidence or reality? Time proportionality causes proportional economic cyclicality and consequently proportionality in the actions of the Fed.




The earthquake science

Earthquake science can be used in markets because of time fractals

The earthquake science working for markets is an opinion as old as the butterfly effect and the study on Sun cycles influencing markets. Xavier Gabaix, assistant professor of economics at MIT, did not say that earthquake causes market behaviour, but that large-scale events in the stock market adhere to distinct patterns which can be witnessed in seismic activity. The MIT professor suggests that economists should borrow the earthquake math from scientists who model natural disasters, the power curve mathematics. The reason that economists are uncomfortable with power laws, says H Eugene Stanley, Boston University is that “unlike the bell curve they are not based on any assumptions about how markets or people work. They are simply curves that fit the data”. Now these ideas are going on since Vilfredo Pareto wrote about the curve first in 1909. Markets are still understanding it and accepting it, 100 years later and we still don’t believe that simple curves rule our life. Human non comprehension of such profound rules and patterns of nature is old news.

The power law

The problem now a century later is that the power law cannot predict when catastrophes happen, but they can predict how often they will occur. According to the Gutenberg-Richter law, for example, an earthquake that is twice as big will be four times as rare. Charles Francis Richter, American seismologist created the Richter magnitude scale. The power law school of thought is not working on the timing problem as they are convinced that power law is not about predicting time, it is just a recurring pattern in nature, which is an unexplainable rule.

Something can’t be understood so it is better to focus on things at hand rather than interpreting the science behind the law of nature. Power law is believed to allow policy-makers to set regulations that better shore up the financial world against extreme events. “It is like Newton’s law of gravity, we don’t understand why it works, it just does, and we use it to build things like rockets,” Stanley says. In short, the scientists have shown that stock markets have a mathematical elegance frequently found in natural systems.

The question here is about the mathematical elegance in everything against the mathematical elegance in time. How can time be inelegant, crude, unsophisticated, unrefined, untasteful, unfashionable and rough? In an interview, Stanley mentioned, “He and his colleagues analysed more than 200 million trades and found that power laws fit better and include the extreme events”. Why did we not test time periods Eugene?

Time decay in earthquakes

According to Plerou and Gopikrishnan, Econophysicists, “Probability of a disastrous economic fluctuation seems to be fairly independent of time period”. Time independence could be an illusion and an idea which could assist physicists to ignore time. In a research published in Seismological letters in February 2007, the authors Mark D Petersen, Tinaquing Cao, Kenneth Campbell and Arthur D Frankek talk about the same earthquake science but from a time dependence aspect. Seismologists are now talking about recurrent time and use elapsed time to calculate earthquake probabilities. Elapsed time is now believed to influence future earthquake events. There is an effort to understand seismic cycles and improve earthquake maps. The researchers say that time dependent models are intuitively appealing.

Though this is an idea in the right direction, it has ground to cover before the scientific community reaches time fractals. We have talked about time decay on prior occasions. This time we are illustrating the time decay in earthquakes. Haiti was in the top destructive earthquakes of all time and has been extensively studied by the US geological survey. We pulled out the minute by minute data from 23 January to 29 January and isolated the time between shocks across the region. The plotted chart was an exponential curve again, suggesting the time (number of days) between shocks was proportionally spread even when smaller time was studied. We get a similar plot when we study earthquake date from 1575 and similar time patterns are seen when we study nuclear tests or any other social and natural activity.

How can time exhibit the same exponential order when the order is believed to be everywhere else? We can either see fractals and patterns all around us, in everything, or accept that time is indeed what gives every living entity, anything which ages, this distinct pattern. Everything from earthquakes, to volcanoes, to cotton prices, to human behaviour and even to the Sun is patterned by time. “When” remains a more important aspect than how often can earthquakes repeat, a crisis occur, a stock rise, or an asset outperform. The focus on “when” can assist us more even if we don’t have a perfect answer. Time is perfect, our interpretation of it can never be.

We started the year attempting to time relative performance. We asked early January, if it was time for Grasim to outperform Nifty? Grasim was at the bottom of numeric rankings on 29 December 2009 and now it is at the top of list. What does this mean? This means that end of December Grasim was ready to outperform Nifty and it did. Long Grasim, short Nifty delivered 13 per cent in January. Now that Grasim has hit a top in rankings, a performance reversal should not be far away, when Grasim starts to underperform Nifty. The anticipated breakdown we have been talking on markets also happened. Metals, small cap and capital goods are ready to underperform the market. Tata Motors and M&M also seem overstretched in performance and should not sustain outperformance against Nifty for long. HDFC’s performance cycles continue to suggest that there is more catch up for the stock against Nifty; the stock should outperform the benchmark. If everything is cyclical like time suggests, research solutions of tomorrow might just simplify things.




From E.D.G. February 1, 2010

Hi folks,

I saw one of your recent reports that compared market trends and earthquakes. The Web site listed above is one where earthquakes are actually being predicted. The forecasts are based on relationships between electromagnetic pulses and past earthquakes. Those data can be fairly accurate. A worldwide Earthquake Advisory was circulated on January 11, 2010, the day before the catastrophic Haiti earthquake. At some time, the main forecasting computer program called “Etdprog.exe” will probably also use data related to the time intervals between earthquakes. A different program discussed at the site called “Wave Chart” provides information concerning those types of data. But they are not yet being used in the actual forecasting program.

Regards, E.D.G.

The Nuclear Decay

Nuclear tests have been conducted from July 1945. Trinity was the first fission device test, first plutonium implosion detonation in the United States. Since then we have seen a series of tests globally with more than nine countries conducting them. The latest one was conducted by North Korea in May 2009. This was the first successful fission device tested by the country.

Nuclear threats are a reality and a cause of concern for the global community. But is this more a factor of free will and arms race? Or are there intricate time patterns between peace and war that dictate the social mood and the events that result from that social behavior?

Patterns of time decay can be seen in this social phenomenon too. Power law practitioners may illustrate that the rule should hold in the number of tests and it does as the decay in Yield suggests. However, why does the same Pareto curve rule hold when we plot the number of days between nuclear tests? There should be something that the practitioners are missing here?

Time is a social construct and we see time through the life and nature around us. Understanding time can not only give a unifying theory to research of a few thousand years, but also help us understand the world we live in. Time evolves, oscillates and continues. Time comes before everything, but we don’t see it. We just feel it. We believe what we see and this is why understanding what is not visible is a challenge.

Nuclear tests are not a creation of autocratic leadership, it’s a result of the changing time, which causes a need to break walls and sometimes build them back.