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# Re: st: zero-inflation and bounds on ARIMA predictions

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: zero-inflation and bounds on ARIMA predictions Date Wed, 19 Dec 2012 19:11:28 +0000

```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
year.

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

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

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

Nick

On Tue, Dec 18, 2012 at 9:22 PM, Winston, Carla A. <Carla.Winston@va.gov> 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 weeks).
>
> 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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