# [R] interrupted time series analysis using ARIMA models

Spencer Graves spencer.graves at pdf.com
Fri Mar 10 19:22:51 CET 2006

```	  Also, are you familiar with Bernhard Pfaff (2006) Analysis of
Integrated and Cointegrated Time Series with R (Springer) and the
companion "urca" package (www.pfaffikus.de)?  I have not used them, but
my cursory review suggests they might do what you want.

hope this helps.
spencer graves

Spencer Graves wrote:

> 	  I'm familiar with Box and Tiao (1975) intervention analysis;  I
> studied time series under Box and Tiao.  I don't know how to do that in
> R, but there must be a way.  Have you looked at the 'dse' bundle?  That
> comes with vignettes that make it relatively easy to learn (or at least
> to learn the capabilities covered in the vignettes).  The models you
> want may not be identified by the names with which you are familiar, but
> I believe they are probably available.  If you try that and still have
> questions, I suggest you consult the posting guide
> (www.R-project.org/posting-guide.html) for help in crafting another
> question that may attract quicker and more useful replies.
>
> 	  I also highly recommend the "zoo" package.  It won't help you solve
> the problem you mentioned, but it might help you keep time stamps with
> your data.  It, too, has a vignette to help people learn the capabilities.
>
> 	  hope this helps.
> 	  spencer graves
>
> Berta wrote:
>
>
>>Dear R-users,
>>Thanks Spencer for your suggestion, i think we are near but still that
>>is not what i am looking for.
>>I think I was not clear using that notation for the impact: (yt= d *
>>yt-1 + w * It ), this yt is not my original series, it is only the impact,
>>the series would be modeled as Yt=yt +Nt, with yt the impact written
>>above and Nt the ARIMA part of the model. Hence, Yt is the series (your
>>lh), and yt the impact.
>>
>>IntReg <- cbind(It=(1:48)>20, It.w=((1:48)>20)*(1:48),
>>It.lh=((1:48)>20)*c(0, lh[-48]) )
>>arima(lh, order = c(1,0,0), xreg=IntReg)
>>
>> I would have for the original series Yt=lh(t)
>>
>>lh(20)=0 + Nt.
>>lh(21)=w + beta1*21 + beta2*lh(20) + Nt
>>lh(22)=w + beta1*22 + beta2*lh(21) + Nt
>>etc.
>>
>>What I am trying to model is a gradual permanent impact, which would
>>
>>lh(t)= impact(t) + Nt
>>lh(t)= w*It + d*yt-1 + Nt
>>
>>lh(20)= 0+ Nt
>>lh(21)= w + Nt
>>lh(22)= d*w + w + Nt
>>lh(22)= (d^2)*w + d*w + w + Nt
>>...
>>lh(n)=(d^n)*w +(d^(n-1))*w +....+(d^2)*w + d*w + w + Nt, which
>>asymptoticaly would be = w/(1-d) + Nt.
>>
>>In that way, I can model the impact not only as an abrupt permanent
>>impact (like a "step") but also as a gradual permanent impact (which
>>grows gradually, as a linear trend or as a parabolic grow trend, or
>>whatever) with just two parameters.  In SAS they are called denominator
>>factors for transfer functions for an input series. I also would like to
>>modelize an abrupt temporary impact (a high pick in the moment of the
>>impact decreasing gradually after it), but hopefully that will be easy
>>after knowing the first.....
>>
>>Any suggestion for implementing this would be very very well received!!
>>
>>Berta.
>>
>>
>>Does the following illustrate the kind of interevention model you want
>>
>>IntReg <- cbind(It=(1:48)>20, It.w=((1:48)>20)*(1:48),
>>               It.lh=((1:48)>20)*c(0, lh[-48]) )
>>      arima(lh, order = c(1,0,0), xreg=IntReg)
>>  hope this helps.
>>  spencer graves
>>
>>Berta wrote:
>>
>> > Hi R-users,
>> >
>> > I am using arima to fit a time series. Now I
>>would like to include an intervention component
>>"It (0 before intervention, 1 after)" using
>>different types of impacts, that is, not only
>>trying the simple abrupt permanent impact (yt =
>>w It ) with the xreg option but also trying with
>>a gradual permanent impact (yt= d * yt-1 + w * It ),
>>following the filosophy of Box and Tiao (1975).
>>Intervention analysis with applications to economic
>>and environmental problems. JASA 70: 70-92.
>> >
>> > Does anybody know where could I find how to
>>incorporate them using the arima comand (or other),
>>or a statistical package which can incorporate it?
>> >
>> > Thanks,
>> >
>> > Berta.
>>
>>
>>
>>
>>
>
>
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