Jan

18

Continuing my study of truncated Levy flights, I have found some paper coming up with the best explanation so far of why variance is necessarily finite. Physically, variance cannot be infinite because there are only a finite number of observations. That's so simple and so grounded in common sense that I am wondering why no one came up with it sooner.

I would like to make another remark. Since, as the Chair and others observed, the market can be quite jumpy in the short term, but converges to normal in the long term, say yearly returns, the central question is: how long before the market converges to normal?

This is somewhat opposite to the Mandelbrotians' worry: how long before a 10-sigma event?

I would be grateful if anyone could point me to good papers about measuring convergence speed.


Comments

Name

Email

Website

Speak your mind

1 Comment so far

  1. NorwegianSpec on January 18, 2007 1:41 pm

    In my humble opinion (with emphis on non-existant rather than infinite population variance):
    An empirical variance (i.e. the empirical second central moment) can allways be calculated from a finite set of observations, it is after all just an average of a sum.

    However, generated from a theoretical distribution with infinite variance, or a from a theoretical distribution where the second central moment does not exist, i.e. does not converge, the empirical variance will not be a consistent estimator of the “true”/theoretical variance (obviously since it does not exist).

    This implies that there is a large probability that the empirical variance generated from several sets of observations from the same poulation might differ widely even when we have many large samples.

    If this happens researchers have a good reason to assume that the true distribution generating the observations does not have a well defined second central moment.

Archives

Resources & Links

Search