However one defines a change in a time series from one time to the next, "errors" in observed values (measurement, effects of extraneous events, etc.) tend to carry over relatively short (daily, weekly, monthly, yearly, for instance) time intervals. This violates the usual assumption in statistical models of independence of residual errors. In practical terms, predictions of values at t when one knows the value at t-1 tend to be much more accurate than predictions in another sample of a time series where neither t or t-1 are known. Time series models adjust for serial correlation of errors by modeling the error term at t as, say, a linear function of the error at t-1, t-2, .....

In 1967, Longley illustrated serial correlation of different time series: http://lib.stat.cmu.edu/datasets/longley

Predicting time series values using another serially correlated time series works great, but how does one predict the values of the correlated time series in advance? S

-----Original Message----- From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of paul wilson Sent: Friday, July 03, 2009 3:19 PM To: SAS-L@LISTSERV.UGA.EDU Subject: Re: Include Predictor that was used to derive the outcome?

Hi Art,

Very interesting point.

What would be advantage of defining DV as "sales in period 2" divided by "sales in period 1" as opposed to "sales in period 2" minus"sales in period 1"?

More importantly, do you see any issues in using "sales in period 1" as a predictor in this sort of a model knowing that it was one of the componets used to derive DV?

Thanks a lot!

________________________________ From: Arthur Tabachneck <art297@NETSCAPE.NET> To: SAS-L@LISTSERV.UGA.EDU; Paul Wilson <paulwilsn@YAHOO.COM> Sent: Friday, July 3, 2009 1:20:12 PM Subject: Re: Include Predictor that was used to derive the outcome?

Paul,

Couldn't you use the delta (i.e., "sales per customer in period 2" / "sales per customer in period 1" -1)as the dv?

Art -------- On Fri, 3 Jul 2009 07:58:43 -0700, paul wilson <paulwilsn@YAHOO.COM> wrote:

>Hi everyone,

I am wondering if there are any issues in terms of biasing my model if I want to include a predictor that was used to derive my dependant variable.

Here is more detail:

Dependant variable is "change in sales volume per customer" meaning "sales per customer in period 1" minus "sales per customer in period 2".

Amongst other things I'd like to investigate if the "amount of sales iper customern period 1" predicts the change in sales. In other words, perhaps customers who used to spend a lot are the ones who had the highest decline in sales� when compared to period 2.

I realize that one needs to be careful not to include a predictor that is really the outcome in discuise, but I'm not sure if that kind of logic applies to this situation.

Thanks a lot!