Date:         Tue, 13 Aug 2002 09:37:06 -0700
Reply-To:     Cassell.David@EPAMAIL.EPA.GOV
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         "David L. Cassell" <Cassell.David@EPAMAIL.EPA.GOV>
Subject:      Re: interpreting time series output
Content-type: text/plain; charset=us-ascii

Shannon <swheatma@FJC.GOV> wrote:
> I have 90 months of data (Jan. 1994-June 2001) that includes filing
> rates for class action cases.
>
> I have used the Time series and Forecasting system in sas to help me
> fit a model.  I have three interventions in May 1996, June 1997, and
> June 1999.  The best fit model is a loglinear trend + seasonal dummy.
> Can someone help me interpret the following data:
>
> Model Parameter            Estimate           Prob>|T|
>
> Intercept                                       2.37
.0001
> Linear Trend                            .002
n.s.
> Seasonal Dummy 1                        -.026
n.s.
> Seasonal Dummy 2                        .056
.07
> Seasonal Dummy 3                        .368
n.s.
> Seasonal Dummy 4                        .311
n.s.
> Seasonal Dummy 5                        .190
n.s.
> Seasonal Dummy 6                        -.007
n.s.
> Seasonal Dummy 7                        .087
n.s.
> Seasonal Dummy 8                        .233
n.s.
> Seasonal Dummy 9                        -.11
n.s.
> Seasonal Dummy 10                       -.197
n.s.
> Seasonal Dummy 11                       .114
n.s.
> May 1996                                        -.397
.04
> June 1997                                       .543
.01
> June 1999                                       .175
n.s.
> Model variance (sigma squared)   .148
>
>
> R-square = .42

First, it looks as though you have a non-significant linear trend.  That
doesn't seem unreasonable.  But it suggests that you might want to
re-fit
the data without a trend component.  If you see a real trend in the
data,
then you needto re-think your model to see how the trend managed to get
masked by the rest of the model features.

Then I'll guess that you have *monthly* adjustment for each of the 12
months
of the year, rather than "seasonal" adjustment.  And it looks like
pretty
much all of your month dummy adjustments are non-significant.  So do
your
data look like there are real seasonal fluctuations?  Do you really
expect
to see seasonal fluctuations in these legal filings?  Is there any
reason to
assume that one month (February?  just guessing here - "seasonal dummy
2")
would have a very slight jump?  A 0.07 shouldn't really be considered
significant anyway, when you're really looking at nearly a dozen dummy
variables
and only one comes out as the least bit significant.  Clearly the
estimate for
"seasonal dummy 2" is a *lot* smaller than some of the other
(non-significant)
monthly dummies - so we have to wonder whether this is at all
meaningful.

It looks to me as if the important part of your model is the three
breakpoints.
You have two of the three turning up as significant, with decent-sized
changes at those breaks.  And your R-squared is a lot better than some
econometric data I've seen in in journals.

Consider re-examining the data in exploratory plots.  Is it reasonable
to
omit the linear trend?  Is it reasonable to drop the dummy variables for
each
month of the year?  Would some manner of cyclic curve express the annual
fluctuations while using up fewer of your degrees of freedom?

Consider re-fitting this with just your three changepoints, and possibly
some sort of curve for the annual features (if they arereal, and not the
result of noise in your data).

HTH,
David
--
David Cassell, CSC
Cassell.David@epa.gov
Senior computing specialist
mathematical statistician