Series: Fat Tails vs Thin Tails

Forecasting elections? Taleb says no

With US elections around the corner, news outlets are…

Tail Risk of diseases in R

Pasquale Cirillo and Nassim Taleb published a short, interesting and important paper on the Tail Risk of contagious diseases. In short, the distribution of fatalities is strongly fat-tailed: thus rendering any forecast, whether is pointwise or a…

Gini Index under Fat-Tails

I have recently been exploring Nassim Taleb’s latest technical book: Statistical Consequences of Fat Tails. In this blogpost, I’ll follow Taleb’s…

Probability Calibration under fat-tails: useless

Probability calibration refers to…

Extreme Value Theory for Time Series

The Fisher-Tippet theorem (a type of CLT for the tail events) rests on the assumption that the observed…

When are GARCH (and friends) models warranted?

In this blogpost, I’ll answer the question, following Nassim Taleb’s latest technical book: Statistical Consequences of Fat Tails, when can we use GARCH (and firends) models? As an example, also following Taleb, I’ll check the resulting conditions with the…

How to not get fooled by the “Empirical Distribution”

With fat-tailed random variables, as Nassim Taleb says, the tail wags the dogs. That is, “the tails (the rare events) play a disproportionately…

Fisher Tippet Th: a “CLT” for the sample maxima

For fat-tailed random variables, the statistical properties are determined by a few observations in the tail. In Nassim Taleb’s words, “the tail wags the dog”. Therefore, it is vital to study the distribution of these few observations. A logical question to ask, then, is: is there a limiting…

LLN for higher p Moments

I have recently been exploring Nassim Taleb’s latest technical book: Statistical Consequences of Fat Tails. In it, we have seen how the Law of Large Numbers for different estimators simply does not work fast enough (in Extremistan) to be…

Central Limit Theorem in Action

I have recently been exploring Nassim Taleb’s latest technical book: Statistical Consequences of Fat Tails. In it, we have seen how the Law of Large Numbers for different estimators simply does not work fast enough (in Extremistan) to be…

R-squared and fat tails

Correlation is not Correlation

To the usual phrase of correlation is not causation, Nassim Taleb often answers: correlation is not correlation. First, just like the mean and PCA, the sample correlation coefficient has persistent small sample effects when variables from Extremistan are involved. These topics are…

Understanding the tail exponent

Power Laws are ubiquitous to describe fat tails, a topic that I’ve been trying to wrap my…

Standard Deviation and Fat Tails

In this post, I’ll continue to explore with Monte-Carlo simulations the ideas in Nassim Taleb’s latest book: Statistical Consequences of Fat Tails.…

What does it mean to fatten the tails?

First, let’s define what we mean by fatter tails.

Spurious PCA under Thick Tails

PCA is a dimensionality reduction technique. It seeks to project the data onto a lower dimensional hyperplane such that as much of the original data variance is preserved.…

Fat vs Thin: does LLN work?

Statistical estimation is based…