And the colored girls say discontinuities, devaney’s chaos, wild tails

The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man. —George Bernard Shaw

Morning Must-Read (so, okay, it’s the afternoon here).

Daniel Kuehn says Howard Reed has gone through the data with “one of the best commentaries” on the Piketty-Giles kerfluffle: it’s all about the discontinuities.

As I demonstrate below, the main difference between the Piketty time series for UK inequality and the Giles time series for UK inequality, is that Piketty corrects his data series to allow for this 23 percentage-point drop (caused by changes in the methodology used to measure the wealth distribution), whereas Giles does not. While Giles has made it clear to me in private correspondence that he was fully aware of the discontinuities in the data series, he chose not to correct his final published data series to allow for them.

On Devaney's Definition of Chaos

An Introduction to Chaotic Dynamical Systems
Robert L. Devaney
Most bell curves have thick tails
Bell Curve Privilege
Mandelbrot’s Natural Wild Random
Overview of Mandelbrot’s Financial Markets
The (Mis)Behaviour of Markets
Mandelbrot’s book

…price changes are very far from following the bell curve. If they did, you should be able to run any market’s price records through a computer, analyze the changes, and watch them fall into the approximate “normality” assumed by Bachelier’s random walk. They should cluster about the mean, or average, of no change. In fact, the bell curve fits reality very poorly.

or, put another way, a long-term memory through which the past continues to influence the random fluctuations of the present.

I call these two distinct forms of wild behavior the Noah Effect and the Joseph Effect. They are two aspects of one reality. One, the other, and usually both can be read in many financial charts. They mix together like two primary colors. The red of one blends with the blue of the other, to produce an infinite palette of purples and violets.

Diagram from Mandelbrot's The (Mis)Behaviour of Markets

…Gaussian math is easy and fits most forms of reality, or so it seems. But with the sharp hindsight provided by fractal geometry, the Gaussian case begins to look not so “normal,” after all. It was so-called only because science tackled it first; as ever in science, there is a healthy opportunism to begin with the problems easiest to handle. But the difference between the extremes of Gauss and of Cauchy could not be greater. They amount to two different ways of seeing the world: one in which big changes are the result of many small ones, or another in which major events loom disproportionately large. “Mild” and “wild” chance, described earlier, are my generalizations from Gauss and Cauchy.

Wild randomness is uncomfortable. Its mathematics is unfamiliar and in many cases remains to be developed. It looks difficult, often requiring elaborate computer simulations rather than a quick punch on a calculator. Unfortunately, the world has not been designed for the convenience of mathematicians. There is much in economics that is best described by this wilder, unpleasant form of randomness — perhaps because economics is about not just the physics of wheat, weather, and crop yields, but also the mercurial moods and unmeasurable anticipations of wheat farmers, traders, bakers, and consumers.


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