Extremal Quantile Regression

Authored by: Victor Chernozhukov , Iván Fernández-Val , Tetsuya Kaji

Handbook of Quantile Regression

Print publication date:  October  2017
Online publication date:  October  2017

Print ISBN: 9781498725286
eBook ISBN: 9781315120256
Adobe ISBN:

10.1201/9781315120256-18

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Abstract

In 1895, the Italian econometrician Vilfredo Pareto discovered that the power law describes well the tails of income and wealth data. This simple observation stimulated further applications of the power law to economic data, including Zipf (1949), Mandelbrot (1963), Fama (1965), Praetz (1972), Sen (1973), and Longin (1996), among many others. It also led to a theory to analyze the properties of the tails of the distributions, so-called extreme value (EV) theory, which was developed by Gnedenko (1943) and deHaan (1970). Jansen and de Vries (1991) applied this theory to analyze the tail properties of US financial returns and concluded that the 1987 market crash was not an outlier; rather, it was a rare event whose magnitude could have been predicted by prior data. This work stimulated numerous other studies that rigorously documented the tail properties of economic data (Embrechts et al., 1997).

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