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List:       sas-l
Subject:    Re: ARIMA Question
From:       Steve Albert <SAlbert () AOL ! COM>
Date:       2002-07-31 22:35:21
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Steve,

   I'll try to help, but first a caveat:  I'm at the office, and most of my time \
series stuff is at home, so I can't look much up.

1.  I agree that your data are probably non-stationary; the distribution at the \
middle is probably significantly different from that at either the start or end.  \
When you say the ACF is decaying over about 7 periods, do you mean 7 weeks?  If so, \
that's a pretty fast decay, not the kind of thing I'd expect to see in, say, a random \
walk model with 130 periods (2.5 yrs) of weekly data.

2.  What is the purpose of your analysis?  What do you want to learn, and how do you \
want to apply it?  Are you trying to build a forecasting model, a model to understand \
the effects of various market forces, a model to optimize policy decisions, or \
something else entirely?

3.  If you have external factors driving sales (competitive drugs being introduced, \
your marketing efforts, competitors' marketing efforts, seasonality of demand, growth \
pattern for introduction of a new product, etc.), I think you need to account for \
those before looking at questions like stationarity.  And don't forget that these \
other factors have their effects not just instantaneously, but over time as well.  \
(Of course, you may be doing all that already.)

4.  I don't know that I'd jump to first-differencing the data, especially if you \
haven't yet considered the other factors above.

5.  I don't know offhand whether the seasonality you report (within month, possibly \
within year) affects your evaluaton of over-differencing -- but I'm pretty sure that \
you do need to account for it in your model.

Building good models for sales over time is complex; besides the statistics, you need \
to understand the market forces involved and their effects over time, consumer \
behavior, the drivers of market demand, etc.  Do you have any colleagues there with \
good econometrics backgrounds, who have lots of experience doing this kind of thing?

Steve Albert
Director of Biostatistics
Spectrum Pharmaceutical Research Corp.
San Antonio, TX
SAlbert at SpectrumCRO dot com


> 
> I'm trying to learn a little bit about ARIMA so I'm modeling some
> weekly sales data (about 2.5 years) using SAS and I've got some
> questions:
> 
> 1) My data are basically an inverted U (sales went up and then came
> back down), I assume this means that my data are non-stationary. I'm
> also drawn to this conclusion by the fact that my sample
> autocorrelation function decreases slowly (over about 7 periods).
> Does this sound correct?
> 
> 2) To remedy the problem, I'm taking the first difference.  The
> resulting series is pretty clearly stationary.  SAS provides the
> inverse autocorrelation function and they say that if the data have
> been over-differenced, then it looks like the ACF from a
> non-stationary series.  Well, the IACF of my differenced series takes
> about 20 periods to decrease to 0. So have I over-differenced my data?
> 
> 3) My weekly data have "seasonal" patterns.  Sales are higher in the
> beginning of the month and decrease after that.  I also have not
> considered the impact of holidays in buying pattermns yet.
> Could the
> seasonal patterns make it look like I'm over-differencing?
> 
> Thanks,
> 
> Steve


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