```Date: Fri, 16 Aug 1996 20:00:08 -0500 Reply-To: GERALD ZUCKIER Sender: "SAS(r) Discussion" From: GERALD ZUCKIER 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. ```

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