Week 3: Avalanches, Rockslides, and Sandpiles, Oh My!

Hello everyone!
If you've been following me up to this point, you're probably starting to wonder what the details of my project are.  I realized this week that while I've been busy talking about the gloriously cool things I've been finding, I have yet to mention what I'm doing on a day-to-day-basis.
So let's do that!

So far, my project has two parts; for the first part, I am working with Dr. Roy Frieden (at the U of A), who has done econophysics research in the past.  He has been directing me to the materials I should read next, in addition to helping explain some of the gnarly statistics.
Dr. Frieden's research (econophysics-related and otherwise) deals primarily in the field of Fisher information, which I feel like I know quite a lot about by this point and plan on sharing with you all in the very near future.

For the second part of the project, I am working with Dr. Srin Manne (also at the U of A).  Dr. Manne is helping me to design an experiment about avalanche dynamics, because as it turns out, the inner workings of avalanches somewhat resemble the inner workings of economic collapses.

I should point out that I'm not referring to snow-based avalanches here, which seem to be the first thing to leap to everyone's mind.  As cool (and terrifying) as those are, they are rather tough for a high school student to model quickly and cheaply.

(While I'm all for Grant's suggestion that I just build a mountain of Eegee's for observation, there's still the melting problem to consider.  And then we'd have a waste of perfectly good Eegee's on our hands, and that's not even justifiable in the name of scientific progress.)

Way to go, Grant.  Now I really want some.

So the avalanches I will be working with are rock-based, rather than snow-based.  This distinction doesn't matter too much, because rock-based avalanches (sometimes called rockslides) actually behave really similarly to snow-based models as long as they "flow" fast enough.
(Avalanches are part of a field called granular physics, which is distinctive because materials following granular behavior behave differently from other "standard" forms of matter, e.g. solid, liquid, and gas.  For example, a rockslide can behave as a liquid entity even though its individual components are solid.)

There are lots of ways to model rocks falling down a hill, it turns out.  One paper I came across actually used  fragmented blocks of coal.  The most famous (and best-explored) model, though, is the sandpile model, which is (surprise, surprise) basically a pile of sand.

Sandpiles (and, by extension, avalanches) are systems that obey self-organized criticality (SOC).  That's a fancy way of saying that the system is attracted to a certain critical point.  For example, if building a sandpile from scratch (as in the above picture), it would collapse in on itself at some critical angle, and stop growing taller.
Classic (non-SOC) examples of "critical points" are defined by an exact parameter.  For example, a phase transition, like liquid turning to gas, occurs at some exact temperature.  However, in SOC systems, the parameters are not exact-- we have no way of knowing which grain of sand will be the one to tip the pile over; it's different for every trial.

In the same way, when dealing with forecasting economic predictions, we might not know exactly which news, action, or other variable will tip the market downwards.  However, we can (hopefully) have some idea of when such a downward spiral might occur, by looking at the patterns.  (Consider the 2008 housing bubble; it followed a familiar and predictable economic pattern.  If we were to somehow repeat the situation, we would still expect some form of market collapse, but it could be from an entirely different variable.)

Obviously, I still have a lot of work to do, as right now I'm working on actually designing the experiment.  I have some ideas; for example, while considerable work has been done with the standard sandpile, which consists of point particles (the grains of sand), Dr. Manne and I are both curious what happens if we were to make a "sandpile" of string particles instead-- e.g. many beaded chains.
Not to worry, though, as soon as I get past the developmental phase and actually start gathering supplies and building the models, I'll be sure to keep you all updated.  Including real live pictures!

Hope you're all having a good week.  Feel free to comment below if you have anything to say!

Week 2: Drunken Meanderings, Fat Tails, and the Markets

Hey guys!  I hope you are all having a fun and productive time at your internships.  This week, I thought I would address some of the earliest research in econophysics.  (Buckle in for another unnecessarily long blog post, everyone!)
Econophysics, it turns out, isn't nearly as innovative as it sounds.  As I mentioned last week, the term was coined almost twenty years ago, (in 1995) but the field's central tenants have been around for much longer than that.  In this blog post I'm going to be talking about Louis Bachelier and his Theorie de la Speculation, or in English, Theory of Speculation.  My onsite adviser, Dr. Frieden, suggested that I start with his work, since it has greatly influenced economic and econophysical theory since its rediscovery in the mid 1950s.

Bachelier, originally trained as a physicist, published his Theory in 1900, dealing principally with the movements of stock prices.  (As data, Bachelier analyzed numbers from the Paris Bourse, then France's principal financial exchange, where he worked for several years in order to pay for his schooling.)

Bachelier's work had two parts that are significant to modern econophysics; I'll explain them both below.  First of all, he derived the mathematical expression of Brownian motion.  Second, he found that the motion of prices in a stock market follows a statistical random walk model.

Since neither of those probably meant very much to you, I'll explain.  Brownian motion is the seemingly random motion of particles suspended in a fluid.  (Liquid or gas.)  A common and easily visualized example is the motion of dust molecules in the air.  This gif (credit to Wikipedia) shows a big particle (e.g. dust particle) colliding with a lot of smaller ones (e.g. gas molecule) and producing random, Brownian motion.

(For those of you who worked with Mr. Young in Multivariable Calc this year, I actually talked to him about this, and it turns out that his work in mathematical modeling is similar to modeling Brownian motion; however, he assumes that the particles or objects he is dealing with have some initial velocity that can impact their final positions.)

When Einstein published a paper in 1905 describing Brownian motion, he didn't know that he was five years too late.  Actually, no one did, as Bachelier's work languished in obscurity for decades despite the fact that he invented a lot of probability theory that was years before its time.

While it is interesting to note that a physicist derived a way to understand our natural world by looking at the economy (which perhaps belies an intrinsic connection), Bachelier's work had a more important side effect that lay in the expression of Brownian motion; if given an infinite amount of time, Brownian motion begins to follow a statistical random walk model.

What's a random walk?
Imagine an incredibly drunk man trying to find his hotel room in a long hall.  Since he's stumbling around, blindly intoxicated and completely clueless, he has an equal probability of stepping forward as stepping backwards.  If he steps forward with his first step, he could step either forward or backward with the next.  You might even say that he's walking... randomly.

It turns out that these random walks follow our buddy the normal curve!  This makes intuitive sense; if our drunk friend starts at hotel room number 50, in principle he could end up at room 10 or room 100 by taking a whole lot of drunk steps forward, or a whole lot backwards.  These "extreme" events are just a lot more unlikely because they would require a certain result (stepping only forward or backwards) many times in a row, similar to flipping a coin 50 times and getting 50 heads.

If you'll recall, though, Bachelier's work was not originally about Brownian motion or random walks at all-- it was about stock prices.  Essentially, Bachelier found that the motion of stock prices follows a random walk.  (It was only as he explored the mathematics of random walks that he "accidentally" solved Brownian motion.  Oops.)

This should be fairly intuitive to us also; we would expect a stock price to fluctuate, but not very much.  What Bachelier was arguing was that small fluctuations in price were much more likely than large ones; statistically speaking, a stock jumping from $1 to $1000 overnight would be incredibly rare; much more rare than the same stock jumping from $1 to $1.05 overnight.  (This becomes important when dealing with something called the Efficient Market Hypothesis, which states that the market is a perfect synthesis of all available information about the value of a stock.  Therefore, the fluctuations would center around a price that was the inherently "correct" value.  I might deal with this more in a future post.)

Also important in his work was the implication that stock markets are inherently random.  After all, if they are  truly random, they follow statistical rules... and they can be predicted with statistical tools.  This was (and is) revolutionary.

It turns out that, unfortunately, Bachelier was wrong, in 2 important ways.  As Maury Osborne discovered in 1959, it is not the prices of stocks that are random, but the relative price changes in stocks.  This makes sense, since investors really care about the percent increase in the value of their stocks more than simply the change in price.  This problem is easily solved by describing the motion of the markets with geometric Brownian motion, which uses the log-normal distribution.  (Taking the logarithm of the difference in prices makes a Gaussian curve.)

Even Osborne didn't have the complete picture; Benoit Mandelbrot (mostly known for discovering fractal geometry) found the next piece of the puzzle, the one that has the biggest implication for modern econophysics.

If we look at the normal curve, we can see that statistical anomalies should not occur very often.  That is, price fluctuations should be relatively stable, with outliers occurring very rarely.  This is not the case in actual market dynamics.  Stocks over a single day typically change less than 2%; a movement of ten standard deviations therefore means a movement of at least 20%.  While Gaussian statistics tells us that such movements should happen once every 10^22 days (longer than the age of the universe) market data shows us that it happens at least once a week.  Something is clearly wrong with our model.

Mandelbrot, while analyzing cotton prices, found that they follow a distribution with fat tails.  Fat-tailed distributions are similar in shape to the normal curve, except that instead of approaching zero probability, their "tails" remain positive for a long time.

Probability of large fluctuations is greater in fat-tailed
distributions

This means, in essence, that improbable events in the markets happen a lot more often than we would imagine.  (Fat tails pop up in physics all the time, incidentally; I'll probably also deal with that in a future post.)

So Bachelier was essentially wrong in his most important argument-- that markets are like random walks. (To his credit, the data that he analyzed at the Paris Bourse did actually follow a random walk model-- perhaps it was especially stable at that time.)  However, he's still relevant to the field, because he established one of the first relationships between physics and the economy, fixed a precedent for analysis of statistical data in the economy, and argued that markets are random.  Economists mostly agree that he got that part right, and that since the markets are random, we can predict their (overall) behavior.  He also laid the groundwork for Mandelbrot to discover the market's fat tails, and thus put us one step closer to understanding some of the latest economic crises.

Sorry again for the pedantic rant, guys.  Have a great week, and feel free to comment!

Week 1: Why Do We Care?

Hi guys!
I hope everyone had a lovely time at Disneyland; if you didn't go, consider yourselves at least a little bit lucky, because I guarantee you got more sleep than I did.

So I'd like to start out by explaining why my project is even relevant in the first place.  Why study Econophysics?  How is it different from or applicable to "normal" economic theory?

When I first started this project way back in October, I found basically an overwhelming number of resources on the Internet that related to this field of study.  One of the things I found was a news editorial by Vincent Fernando about Econophysics, which can be found at
http://www.businessinsider.com/failed-economists-concoct-new-econophysics-2010-8
(I spent about a half hour trying different variations of Google searches before I thought to look in my browser history.  D'oh.)

For those too lazy to read the whole thing, the most important sentence is probably,
"[Econophysics is flawed] because economics is a social phenomenon, like politics, or social development.  It's not physics, and it's not chemistry."

The idea being that we cannot predict the behavior of humans (and thus the markets) using laws derived to predict the behavior of particles and other physical phenomenon like earthquakes.  This is by virtue of the fact that, unlike electrons, humans make decisions that are emotion-based, occasionally illogical, and that depend on limited information.

(Let's forget for just a moment that most modern macroeconomic theory is based on rational choice, which states that people make decisions that are the most prudent, logical, and likely to provide them with the greatest benefit in their own self-interest.  How much more particle-like and/or oversimplified can we get here?)

(If you can't tell, I'm not the biggest fan of rational choice theory, mostly because the only place I've ever seen people act 100% in their own self-interest is in the BASIS parking lot.)

Mr. Fernando's claim, however, completely misunderstands the nature and purpose of Econophysics.

Let's look at a definition by Dr. Roy Frieden, my onsite-advisor, who has analyzed this topic with regard to optical statistics:

"[The basic premise of econophysics] is that the same mathematical and phenomenological insights that are used to provide unification for complex physical systems can now apply to problems of economics and finance."  (Frieden and Gatenby, 2007, p. 43).

Dr. Frieden is not claiming that people are atoms, or that we should expect them to behave rationally and logically all the time.  He is claiming that the overall behavior of markets and economic systems can be compared with behaviors in the natural sciences.  He is claiming that the same tools (e.g. statistical models, physical models and theories, etc.) can be applied to understand markets better.

It is important to make the distinction, as Mark Buchannon does quite well, that "The most important lesson of modern physics is that it is often not the properties of the parts that matter most, but their organization, their pattern and their form."  (Buchannon, 2007, p. 10).  He goes on to say that "no study of soil or stones could perfectly explain [the circular patterns that form due to weather and earth movements] just as no study of air molecules on their own could help anyone understand a hurricane." (p. 12)

In much the same way, while humans as individuals are very complex and ruled by emotion and unpredictability, that doesn't mean that their actions as a whole can't be predicted or at least understood.  Current Macroeconomic theory aims to do exactly that, after all--  there is no reason that physics, a field dedicated to unifying and modeling smaller parts of a whole, cannot at least attempt it.

Perhaps the one thing that Mr. Fernando got completely correct in his article was that current macroeconomic theory, bluntly put, isn't working very well.  As the economic consultancy London Economics, led by John Kay, points out, "It is a conventional joke that there are as many different opinions about the future of the economy as there are economists.  The truth is quite the opposite.  Economic forecasters... all say more or less the same thing at the same time... The differences between forecasts are trivial compared to the differences between forecasts and what actually happens... what they say is almost always wrong... the consensus forecast failed to predict any of the most important developments in the economy over the past seven years."

What I hope to evaluate with this project is not only the usefulness of these comparisons to physics but also the extent to which they can be applied.  So far, it seems to me that a further study into econophysics can, at worst, only broaden our knowledge of current economic workings, and at best, can be used to permanently change our view of the markets, especially given the current misunderstandings going on in economics.

(Note: Mr. Fernando is also incorrect in his assumption that the field of econophysics is somehow "new."  While the term was coined fairly recently-- in 1995, still roughly fifteen years before his editorial was published-- the field has been around for much longer than that, and has influenced modern economic theory in several important ways.  I will hopefully cover those in the near future.)

Sorry this is a bit long...
Have a great week everyone!  Please feel free to comment!