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 start with my old crusade against "quants" (people like me who do mathematical work in finance), economists, and bank risk managers, my prime perpetrators of iatrogenic risks (the healer killing the patient). Why iatrogenic risks? Because, not only have economists been unable to prove that their models work, but no one managed to prove that  the use of a model that does not work is neutral, that it does not increase blind risk taking, hence the accumulation of hidden risks.


Figure 1 -  My classical metaphor: A Turkey is fed for a 1000 days--every days confirms to its statistical department that the human race cares about its welfare "with increased statistical significance". On the 1001st day, the turkey has a surprise.

(...)

By the "narrative fallacy" the turkey economics department will always manage to state, before thanksgivings that "we are in a new era of safety", and back-it up with thorough and "rigorous" analysis. And Professor Bernanke indeed found plenty of economic explanations--what I call the narrative fallacy--with graphs, jargon, curves, the kind of facade-of-knowledge that you find in economics textbooks. (This is the find of glib, snake-oil facade of knowledge--even more dangerous because of the mathematics--that made me, before accepting the new position in NYU's engineering department, verify that there was not a single economist in the building. I have nothing against economists: you should let them entertain each others with their theories and elegant mathematics, and help keep college students inside buildings. But beware: they can be plain wrong, yet frame things in a way to make you feel stupid arguing with them. So make sure you do not give any of them risk-management responsibilities.)



In the long run, we're all dead. John Maynard Keynes
by Jerome a Paris (etg@eurotrib.com) on Sun Sep 21st, 2008 at 02:05:55 PM EST
but not particularly convincing. The turkey metaphor is a rhetorical trick, the mathematical appendix is incoherent, and there's no mention of Extreme Value Theory, which is surprising in an article discussing the supposed impossibility of modelling extremes.

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$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Mon Sep 22nd, 2008 at 03:03:48 AM EST
[ Parent ]
Um, given that estimates based on extreme value theory have to be done on very few data points, the reliability of the estimates must be a huge issue.

A vivid image of what should exist acts as a surrogate for reality. Pursuit of the image then prevents pursuit of the reality -- John K. Galbraith
by Migeru (migeru at eurotrib dot com) on Mon Sep 22nd, 2008 at 04:41:19 AM EST
[ Parent ]
It would be highly inefficient to perform estimates merely on a few extreme values. If one estimates parameters using all threshold exceedances however, then there's a lot more data available to use. That's the idea anyway, together with the fact that the possible asymptotics belong to on of three families of EV distributions: Gumbel, Frechet or Negative Weibull.

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$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Mon Sep 22nd, 2008 at 05:00:21 AM EST
[ Parent ]
The basic argument against the practicality of extreme value theory is this:
A Simple Proof Of Unpredictability In The Fourth Quadrant

I show elsewhere that if you don't know what a "typical" event is, fractal power laws are the most effective way to discuss the extremes mathematically. It does not mean that the real world generator is actually a power law--it means you don't understand the structure of the external events it delivers and need a tool of analysis so you do not become a turkey. Also, fractals simplify the mathematical discussions because all you need is play with one parameter (I call it "alpha") and it increases or decreases the role of the rare event in the total properties.

Um, forget about "fractal" - Taleb is in thrall to Mandelbrot. He's simply talking about power-law (and hence scale free and so "fractal") fat tails - e.g., Pareto. "Alpha" is the exponent of the power law
For instance, if you move alpha from 2.3 to 2 in the publishing business, the sales of books in excess of 1 million copies triple!  Before meeting Benoit Mandelbrot, I used to play with combinations of scenarios with series of probabilities and series of payoffs filling spreadsheets with clumsy simulations; learning to use fractals made such analyses immediate. Now all I do is change the alpha and see what's going on.
Fair enough, writing for laymen. Here's the rub:
Now the problem: Parametrizing a power law lends itself to monstrous estimation errors (I said that heavy tails have horrible inverse problems). Small changes in the "alpha" main parameter used by power laws leads to monstrously large effects in the tails. Monstrous.
This is a more jargon-laden restamement of if you move alpha from 2.3 to 2 in the publishing business, the sales of books in excess of 1 million copies triple!
And we don't observe the "alpha. Figure 5 shows more than 40 thousand computations of the tail exponent "alpha" from different samples of different economic variables (data for which it is impossible to refute fractal power laws). We clearly have problems figuring out what the "alpha" is: our results are marred with errors. Clearly the mean absolute error is in excess of 1 (i.e. between alpha=2 and alpha=3). Numerous papers in econophysics found an "average" alpha between 2 and 3--but if you process the >20 million pieces of data analyzed in the literature, you find that the variations between single variables are extremely significant.
The fact is that, assuming independent, identically distributed observations, the probability that the next observation will be larger than the past N observations is 1/(N+1) - with no upper limit for the confidence interval. That's the non-parametric view. The problem with the parametric view is that with power-law fat tails, as taleb correctly points out, small estimation errors on the parameter lead to huge variations in the confidence interval for the next observation conditional on it exceeding all previous observations.

A vivid image of what should exist acts as a surrogate for reality. Pursuit of the image then prevents pursuit of the reality -- John K. Galbraith
by Migeru (migeru at eurotrib dot com) on Tue Sep 23rd, 2008 at 05:54:05 AM EST
[ Parent ]
Wikipedia: Pareto distribution and Zipf's law.

A vivid image of what should exist acts as a surrogate for reality. Pursuit of the image then prevents pursuit of the reality -- John K. Galbraith
by Migeru (migeru at eurotrib dot com) on Tue Sep 23rd, 2008 at 06:01:12 AM EST
[ Parent ]
Would you consider a diary debating Taleb's claims in some detail?

A vivid image of what should exist acts as a surrogate for reality. Pursuit of the image then prevents pursuit of the reality -- John K. Galbraith
by Migeru (migeru at eurotrib dot com) on Mon Sep 22nd, 2008 at 05:00:26 AM EST
[ Parent ]
I could, it would take a bit of time to do right, though (=> not right now :)

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$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Mon Sep 22nd, 2008 at 05:04:28 AM EST
[ Parent ]
See the diary

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$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Wed Sep 24th, 2008 at 01:46:04 AM EST
[ Parent ]
Thanks.

A vivid image of what should exist acts as a surrogate for reality. Pursuit of the image then prevents pursuit of the reality -- John K. Galbraith
by Migeru (migeru at eurotrib dot com) on Wed Sep 24th, 2008 at 02:17:39 AM EST
[ Parent ]

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