q-fin updates on arXiv.org
Wed, 29 Jan 2020 06:01:46 GMT language
The book investigates the misapplication of conventional statistical
techniques to fat tailed distributions and looks for remedies, when possible.
Switching from thin tailed to fat tailed distributions requires more than
"changing the color of the dress". Traditional asymptotics deal mainly with
either n=1 or $n=infty$, and the real world is in between, under of the "laws
of the medium numbers" --which vary widely across specific distributions. Both
the law of large numbers and the generalized central limit mechanisms operate
in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable
basins of convergence.
A few examples:
+ The sample mean is rarely in line with the population mean, with effect on
"naive empiricism", but can be sometimes be estimated via parametric methods.
+ The "empirical distribution" is rarely empirical.
+ Parameter uncertainty has compounding effects on statistical metrics.