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Date:         Thu, 19 Apr 2007 11:14:39 -0500
Reply-To:     "Huang, JS" <Huang.JS@PRINCIPAL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         "Huang, JS" <Huang.JS@PRINCIPAL.COM>
Subject:      Re: calculating rolling standard deviation
Comments: To: PBilin <pbilin@GMAIL.COM>
In-Reply-To:  A<1176994361.512818.292920@n76g2000hsh.googlegroups.com>
Content-Type: text/plain; charset="us-ascii"

See if the following fits your need.

data my_data; input observation_no p; datalines; 1 1 1 2 1 3 1 4 2 3 2 5 2 10 2 13 2 18 ;

data Temp; retain SumOfX SumOfX2 xCount; set my_data; by observation_no; if first.observation_no then do; xCount=1; SumOfX=p; SumOfX2=p**2; end; else do; xCount=xCount+1; SumOfX=SumOfX+p; SumOfX2=SumOfX2+p**2; end; run;

data Result(keep=observation_no p PopulationStdDev Last3PopulationStdDev); set Temp; PopulationStdDev=((SumOfX2-SumOfX**2/xCount)/xCount)**0.5; Last3Observation_no=lag3(observation_no); Last3SumOfX2=lag3(SumOfX2); Last3SumOfX=lag3(SumOfX); if observation_no eq Last3Observation_no then do;

Last3PopulationStdDev=(((SumOfX2-Last3SumOfX2)-(SumOfX-Last3SumOfX)**2/3 )/3)**0.5; end; run;

proc print data=Result; run;

***** Output ***** The SAS System 08:18 Thursday, April 19, 2007 50

observation_ Population Last3Population Obs no p StdDev StdDev

1 1 1 0.00000 . 2 1 2 0.50000 . 3 1 3 0.81650 . 4 1 4 1.11803 0.81650 5 2 3 0.00000 . 6 2 5 1.00000 . 7 2 10 2.94392 . 8 2 13 3.96074 3.29983 9 2 18 5.41849 3.29983

-----Original Message----- From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of PBilin Sent: Thursday, April 19, 2007 9:53 AM To: SAS-L@LISTSERV.UGA.EDU Subject: Re: calculating rolling standard deviation

One more question. I am trying to adjust the proposed code to calculate rolling standard deviation for the last 3 observations only.

Here is the adjusted code:

data Result(drop=SumOfX SumOfX2 xCount); retain SumOfX SumOfX2 xCount sumofx_12 sumofx2_12 xcount_12 xcount_new; set my_data; by observation_no; if first.observation_no then do; xCount=1; SumOfX=p; SumOfX2=p**2; end; else do; xCount=xCount+1; SumOfX=SumOfX+p; SumOfX2=SumOfX2+p**2; end; q=sumofx; w=sumofx2; e=xcount; sumofx_12=lag3q); sumofx2_12=lag3(w); sums=q-sumofx_12; sums2=w-sumofx2_12; xcount_12=lag3(e); xcount_new=xcount-xcount_12; PopulationStdDev=((SumOfX2-SumOfX**2/xCount)/xCount)**0.5;

PopulationStdDev_2=((Sums2-Sums**2/xcount_new)/xcount_new)**0.5;

run;

The idea is to take a difference between sumofx for current observation and for observation 3 periods before. Unfortunatelly, the code is not working properly.

Would appreciate your comments!

Paul

On Apr 19, 10:50 am, PBilin <pbi...@gmail.com> wrote: > Thank you all for your help! The solutions work very neatly! > > Paul > On Apr 18, 10:17 pm, Huang...@PRINCIPAL.COM ("Huang, JS") wrote: > > > Dan: > > > It is a neat way to calculate sum of square of deviation from the > > mean iteratively. For those who are interested in the derivation > > here is the proof. > > > In the following mu_n denote mean of the first n terms and > > mu_(n-1) mean of the first n-1 terms. > > > Sum{(X_i - mu_n)**2, i=1 to n} - Sum{(X_i - mu_(n-1))**2, i=1 to > > n-1} = Sum{(X_i - mu_n)**2, i=1 to n-1} + (X_n - mu_n)**2 - Sum{(X_i

> > - mu_(n-1))**2, i=1 to n-1} = Sum{((X_i - mu_(n-1)) + (mu_(n-1) - > > mu_n))**2, i=1 to n-1} + (X_n - > > mu_n)**2 - Sum{(X_i - mu_(n-1))**2, i=1 to n-1} = Sum{(X_i - > > mu_(n-1))**2 + 2*(X_i - mu_(n-1))*(mu_(n-1) - > > mu_n)+(mu_(n-1) - mu_n)**2, i=1 to n-1} + (X_n - mu_n)**2 - Sum{(X_i

> > - mu_(n-1))**2, i=1 to n-1} = Sum{(X_i - mu_(n-1))**2, i=1 to n-1} +

> > 2*(mu_(n-1) - mu_n)*Sum{(X_i - mu_(n-1)), i=1 to n-1} + > > (n-1)*(mu_(n-1) - mu_n)**2 + (X_n - mu_n)**2 - Sum{(X_i - > > mu_(n-1))**2, i=1 to n-1} > > > The first and last terms cancel each other and Sum{(X_i - > > mu_(n-1)), > > i=1 to n-1} = 0 and hence the above can be simplified to: > > (n-1)*(mu_(n-1) - mu_n)**2 + (X_n - mu_n)**2 = (n-1)*(mu_(n-1) - > > mu_n)*(mu_(n-1) - mu_n) + (X_n - mu_n)**2 = -(X_n - mu_n)*(mu_(n-1) > > - mu_n) + (X_n - mu_n)**2 (See (***) below for derivation.) = (X_n -

> > mu_n)*(-(mu_(n-1) - mu_n) + (X_n - mu_n)) = (X_n - mu_n)*(X_n - > > mu_(n-1)) = (X_n - mu_(n-1))*(X_n - mu_n) > > > We obtained > > Sum{(X_i - mu_n)**2, i=1 to n} - Sum{(X_i - mu_(n-1))**2, > > i=1 to n-1} = (X_n - mu_(n-1))*(X_n - mu_n) Or > > Sum{(X_i - mu_n)**2, i=1 to n} = Sum{(X_i - mu_(n-1))**2, > > i=1 to n-1} + (X_n - mu_(n-1))*(X_n - mu_n) > > > This is what is used in Dan's statement > > > v + (value_x - prior_mean) * (value_x - mean); > > > QED. > > > (***) > > (n-1)*(mu_n-1) - mu_n) > > = (n-1)*mu_(n-1) - n*mu_n + mu_n > > = Sum{X_i, i=1, n-1} - Sum{X_i, i=1, n} + mu_n = -X_n + mu_n = -(X_n

> > - mu_n) > > > Replacing the first > > > -----Original Message----- > > From: SAS(r) Discussion [mailto:S...@LISTSERV.UGA.EDU] On Behalf Of > > > Nordlund, Dan (DSHS/RDA) > > Sent: Wednesday, April 18, 2007 3:12 PM > > To: S...@LISTSERV.UGA.EDU > > Subject: Re: calculating rolling standard deviation > > > > -----Original Message----- > > > From: SAS(r) Discussion [mailto:S...@LISTSERV.UGA.EDU] On Behalf > > > Of PBilin > > > Sent: Wednesday, April 18, 2007 10:45 AM > > > To: S...@LISTSERV.UGA.EDU > > > Subject: calculating rolling standard deviation > > > > hello, > > > > I am trying to calculate a rolling standard deviation for a > > > variable > > > value_x: > > > > date obs_number value_x stdandard_deviation > > > 01012000 1 1 std(1) > > > 01022000 1 1.2 std(1,1.2) > > > 01032000 1 12 std(1,1.2,12) > > > 01042000 1 5 std(1,1.2,12,5) > > > 01052000 1 6 .... > > > 01012000 2 42 > > > 01022000 2 1.422 > > > 01032000 2 15232 > > > 01042000 2 65 > > > 01052000 2 63 > > > > As you see, each next value of standard_deviation uses one extra > > > observation of value_x. > > > > Would appreciate your help! > > > Paul, > > > I see you have at least one solution, let me add another (which I > > learned some time ago from the BMDP software documentation). > > Depending on the number of observations and the nature of the data > > this method could be more accurate than using the common > > computational formula, sum(x**2)-sum(x)**2/N, for the sums of > > squares. You can drop whatever variables you don't want to keep. > > It would need to be modified slightly if you have any missing data, or if you wanted to use weighted data. > > > data want; > > set your_data; > > retain n mean v 0; > > n + 1; > > prior_mean = mean; > > mean + (value_x - mean)/n; > > v + (value_x - prior_mean) * (value_x - mean); > > standard_deviation = (v/(n-1))**.5 ; run; > > > Hope this is helpful, > > > Dan > > > Daniel J. Nordlund > > Research and Data Analysis > > Washington State Department of Social and Health Services Olympia, > > WA > > 98504-5204 > > > -----Message Disclaimer----- > > > This e-mail message is intended only for the use of the individual > > or entity to which it is addressed, and may contain information that

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