# [R] Running median

Martin Maechler maechler at stat.math.ethz.ch
Tue Aug 20 14:38:38 CEST 2002

```>>>>> "DavidB" == David Brahm <brahm at alum.mit.edu>
>>>>>     on Mon, 19 Aug 2002 20:18:47 -0400 writes:

DavidB> I have a Date x Stock (223 x 520) matrix of "trading
DavidB> volume".  I can calculate a 5-day (past) average in

R> apply(vol, 1, filter, filter=c(0, rep(1/5,5)), sides=1)

DavidB> I would like to do the same with a 5-day median,
DavidB> e.g.:

R> mymed <- function(x, n=5) {
R>   r <- rep(NA, length(x))
R>   for (i in (n+1):length(x)) r[i] <- median(x[i-(1:n)])
R>   return(r)
R> }

R> apply(vol, 1, mymed)

DavidB> only faster (the above takes 65 seconds).  Is there
DavidB> already a function (or some C code) to do this?  Any
DavidB> clever way to vectorize it?

DavidB> smooth() in package "eda" with kind="3" calculates a
DavidB> running median of 3 values, so I may start with the
DavidB> code in library/eda/src/smooth.c, but it doesn't
DavidB> generalize easily to N values.  Also, decmedian() in
DavidB> package "pastecs" may be relevant, but doesn't seem
DavidB> any faster than my naive code.

(yes).

On the "R Developer page", there are TODO lists of several R core members.
Mine (http://developer.R-project.org/TODO-MM.html) contains an item

MM> Running Medians for library(modreg) :
MM>   We need a fast robust smoother; lowess() is not robust.
MM> 	(a non-release of a package "runmed" is available;
MM> 	 need to write a short paper on what I found ....)

There two big steps making it much faster :
1) move to compiled code
2) use a smarter algorithm -- I have two versions :
a. There is a first idea of making it fast which dates back to
Friedman & Stuetzle's work on projection pursuit in the 80s.

b. Computing `running median of k' for larger `k' :
To make this really fast (asymptotically optimal),
Haerdle & Steiner published a paper on how to do this
and Berwin Turlach has programmed it (or just translated
their program).

Yes, as I say above, this should eventually become part of the
"modreg" package.

--
Martin Maechler <maechler at stat.math.ethz.ch>	http://stat.ethz.ch/~maechler/
Seminar fuer Statistik, ETH-Zentrum  LEO C16	Leonhardstr. 27
ETH (Federal Inst. Technology)	8092 Zurich	SWITZERLAND
phone: x-41-1-632-3408		fax: ...-1228			<><
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