[R] Hodrick-Prescott Filter: Special Case of smooth.spline()

Roger Koenker roger at ysidro.econ.uiuc.edu
Fri Dec 14 15:12:02 CET 2001

On Fri, 14 Dec 2001, Martin Maechler wrote:

> Exactly because I found I did want to get at the lambda
> used, in R 1.4 (to be released in a few days) `lambda' at least
> is returned as well as spar and the details section contains
> even more details about the relation of `spar' and `lambda'
This one of the more charming features of R...the psychic powers
of the core group to anticipate questions and resolve problems never
ceases to amaze.

>     Roger> For those of you (if any) who are wondering what the
>     Roger> Hodrick-Prescott filter is: in effect it is the
>     Roger> special case of the (Reinsch) cubic smoothing spline
>     Roger> for an equally spaced time series.  HP claim that for
>     Roger> (typical quarterly economic time-series) lambda can
>     Roger> be chosen to be 1600, and (amazingly) this has become
>     Roger> a default smoother in some circles of
>     Roger> macroeconometrics.
> interesting... this means that one uses the same (kernel-) equivalent
> smoothing window for all quartely time series?  Wouldn't this
> mean that (a combination of) the smoothness of the true
> underlying function m(x) and the (local) variance sigma(x) was
> assumed to be (almost) a universal constant?

Precisely, but some people believe in the tooth fairy too.  Or for
that matter in the existence of that "true underlying function" ... ;-).

url:	http://www.econ.uiuc.edu		Roger Koenker
email	roger at ysidro.econ.uiuc.edu		Department of Economics
vox: 	217-333-4558				University of Illinois
fax:   	217-244-6678				Champaign, IL 61820

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