re: Re: st: Generalized Error Distribution (GED) in Stata

[Christopher Baum <kit.baum@bc.edu>]

<>
Stas said

I wonder who came up with that name for a distribution. Since it is
not in the poster of univariate distributions (see

http://dx.doi.org/10.1198/000313008X270448),
 nor it is in Johnson &
Kotz encyclopedias, this distribution very likely does not generalize
as much as it promises. If there is no existing implementation, you
should write your own; that's what Stata is about.

This distribution is well known in the time series econometrics literature, and implemented by most programs that 
estimate ARCH/GARCH models -- including Stata. See [TS] arch and its distribution(ged) option. Stata's documentation
cites 

Nelson, D. B. 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59: 347–370.

as using this distribution.  He in turn cites works by Harvey (1981), Box and Tiao (1973). In the Econometrica article, Nelson gives the GED density function, which involves the gamma function and the incomplete gamma function. 

Wikipedia's article(http://en.wikipedia.org/wiki/Generalized_normal_distribution) suggests that it is known as the Generalized normal distribution, the Exponential power distribution, etc. 

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
                              An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
   An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html


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