The Earthquake Science

The Earthquake Science

Earthquake science is relevant for stock markets.

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 behavior, 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 only 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 the 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. The 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 analyzed more than 200 million trades and found that power laws fit better and include the extreme events”.

According to Plerou and Gopikrishnan, Econophysicists, “Probability of a disastrous economic fluctuation seems to be fairly independent of the 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 or a durational symmetry. The author has talked about time decay on prior occasions. 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 durational data was an exponential curve again, suggesting the time (number of days) between shocks was proportionally spread even when the 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 a statistical behaviour when the order is believed to be everywhere else? We can either see structure 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 connected in time. “When” remains a more important aspect than how often can earthquakes repeat, a crisis occurs, 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.

First published on Jan 2, 2010