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RE: st: zero-inflation and bounds on ARIMA predictions

From   "Winston, Carla A." <>
To   <>
Subject   RE: st: zero-inflation and bounds on ARIMA predictions
Date   Fri, 21 Dec 2012 10:31:29 -0800

Thanks very much, the references were fun and helpful.  With this reply,
I close the thread unless folks wish to comment further.  

For interest, telephone call and admission data are both for influenza,
highly seasonal.  The mechanism producing zeros is dips in influenza
admissions at certain times of year.  I have used sine and cosine for
modeling influenza in the past, but this seemed different in that we
were interested in the relationship between two time series with
approximately the same seasonality.  Our objective was primarily to
assess the similarity of the two time series using cross-correlation.  I
began to play with models with the idea of looking at predictions based
on lags of the dependent variable and telephone calls as a "predictor"
variable.  I have now implemented a plain old Poisson regression and the
fit is very good even without the trigonometric predictors.  

Thank you.  

-----Original Message-----
[] On Behalf Of Nick Cox
Sent: Wednesday, December 19, 2012 11:11 AM
Subject: Re: st: zero-inflation and bounds on ARIMA predictions

These two families of model are not really comparable. One focuses on
data as a time series, while the other focuses on a response with a
supposed distribution.

Without knowing what your precise objectives are it seems that you
have strong seasonality. In the case of weeks, 52 weeks won't work
optimally to catch all seasonality as over a period of several years
the number of weeks in a year will average more than 52 and some
seasonality will not be exact as weather will vary for a given time of

Moreover, what mechanism produces zeros? Is it partly structural that
admissions are not allowed or mostly or entirely stochastic that the
number of admissions dips at certain times of year? (Specifically,
what leads you to suppose _inflation_?)

For such data I would typically start with Poisson models and sine and
cosine functions based on time of year. I wouldn't start with time
series models.

See also

SJ-9-2  gr0037  . . . . . . . .  Stata tip 76: Separating seasonal time
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N.
J. Cox
        Q2/09   SJ 9(2):321--326                                 (no
        tip on separating seasonal time series

SJ-6-4  st0116  . . . .  Speaking Stata: In praise of trigonometric
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N.
J. Cox
        Q4/06   SJ 6(4):561--579                                 (no
        discusses the use of sine and cosine as predictors in
        modeling periodic time series and other kinds of periodic

SJ-6-3  gr0025  . . . . . . . . . . . . Speaking Stata: Graphs for all
        (help cycleplot, sliceplot if installed)  . . . . . . . . .  N.
J. Cox
        Q3/06   SJ 6(3):397--419
        illustrates producing graphs showing time-series seasonality


On Tue, Dec 18, 2012 at 9:22 PM, Winston, Carla A.
<> wrote:
> Dear friends, I am using Stata 12.1 for a regression model of
healthcare telephone calls predicting hospital admissions.  Admissions
and calls can never be non-negative.  The admissions are zero-inflated
and stationary; calls are stationary.  The data are in weeks, are
second-order autoregressive, and show annual seasonality (i.e., at 52
> arima admissions calls, sarima(2,0,0,52) vce(robust) diffuse
> I have been working to create a seasonally adjusted model and am
generally happy with the above, but predictions include negative numbers
for some of the weeks when observed admissions are zero.  Would it be
better to use a negative binomial or zero-inflated Poisson model rather
than ARIMA?  Or is there another way to bound the ARIMA?  I like the
ease of the ARIMA seasonal coding, but want to ensure that model
predictions are never < 0.  I have also examined -prais- and -vecm- but
did not settle on a satisfactory way to account for the

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