Date:         Fri, 16 Aug 1996 20:00:08 -0500
Reply-To:     GERALD ZUCKIER <ZUCKIER@CHIME.ORG>
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         GERALD ZUCKIER <ZUCKIER@CHIME.ORG>
Subject:      Re: rolling averages
In-Reply-To:  <01I8AUQ57LUEQUEQ3Y@HARPO.CHIME.ORG>

OK, since apparently all the math whizes have actual lives and meaningful work
to do, and/or I'm more obsessed with this than the rest of you, I worked out the
coefficients for the first few terms, assuming the first 4 means to be
calculated on nonmissing data only, reasonably enough:
 
TERM     X1   X2   X3   X4   X5   X6   X7   X8   X9  X10  X11
   1   1.00
   2   0.50 0.50
   3   0.50 0.17 0.33
   4   0.50 0.17 0.08 0.25
   5   0.50 0.17 0.08 0.05 0.20
   6   0.40 0.20 0.10 0.06 0.04 0.20
   7   0.38 0.14 0.12 0.07 0.05 0.04 0.20
   8   0.36 0.13 0.08 0.09 0.06 0.05 0.04 0.20
   9   0.33 0.13 0.08 0.05 0.07 0.06 0.05 0.04 0.20
  10   0.29 0.12 0.07 0.05 0.04 0.07 0.06 0.05 0.04 0.20
  11   0.27 0.10 0.07 0.05 0.04 0.04 0.07 0.06 0.05 0.04 0.20
 
In precise mathematical terms, I generally don't like the looks of this. Instead
of a smooth decay over time there is more of an 'echo' phenomenon where the
influence of a data value increases as it recedes into the past from T(-1) to
T(-4), then an echo of the echo, etc. As a corollary of this, the startup
transient sort of hangs on for a long time.
 
John, show this table to your managers and ask them if this is what they had in
mind. If they say yes, we can send the whole episode in to appear as a Dilbert
strip. If not, try and convince them to go for my aforementioned exponential
filter, AVEX = MEAN(X,AVEX). It's a moral issue at this point; truth through
mathematics.