Re: Forecasting by ARIMA model

From: neeru (neeru_jaiswal_at_yahoo.com)
Date: 01/25/05 

Date: Tue, 25 Jan 2005 18:14:55 +0000 (UTC)

Dear Dave,
Thanks for ur reply.
At present I am using nonseasonal ARIMA model. I have understood the
model building part,But I am not clear about the forecasting part.

For example :If error terms follows NID(0, 0.2).The ARIMA(1,1,1)
equation estimated by the data is
y(t)=0.921+0.831*y(t-1)+e(t)-0.341*e(t-1). The if I have to get
y(t+1), y(t+2)....up to 30 steps,what values for e(t) and e(t-1)
should be substituted in the above equation.

As of my understanding I should keep e(t)'s zero for the futire time
steps t+1,t+2,..., But In this case I will get the equation
y(t+3)=0.921+0.831*y(t+2). this will be a monotonic decreasing series.
But it should be fluctuating series.

or I should get values of e(t) from the distribution. Then It is again
a problem from me how to get the values from that.

Can u please tell me where am I wrong?

Thanks,
Neeru

dave@autobox.com wrote:
>Neeru,
>
>I believe your understanding of the model is correct and in specific
>
>y(t)=a1*y(t-1)+a2*y(t-2) + b1*e(t-1)+ konstant
>
>Now in general that konstant might better be presented as
>
>konstant= c1*t1+c2*t2+..... + d1*l1+d2*l2 +.... + c1*sp1+c2*sp2 + ...
+
>d1*p1+d2*p2 +....
>
>
>where t1 might be 1,2,3,4,.....the counting numbers
>t2 0,0,0,0,0,...1,2,3,... reflecting a change
>in trend
>etc..
>
>l1 might be 0,0,0,0,0,....,0,1,1,1,1 reflecting a change in level
>l2 0,0,0,0,0,0,0,0,0,0,....1,1,1,1, reflecting yest a
>second change in level
>
>sp1 might be a seasonal pulse reflecting a deterministic component
say
>in July of each year
>
>0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,...... where the onset
of
>the SEASONAL PULSE may not be the beginning of the series but at some
>later point
>
>similarly other SEASONAL INDICATORS might be harvested
>
>and
>
>p1 is a PULSE VARIABLE t a particular point in time reflecting an
>anomaly or an expected result reflecting an OMITTED CAUSE VARIABLE.
>
>
>In summary your model might need to include IDENTIFIABLE INTERVENTION
>VARIABLES which reflect omitted determinstic structure and can often
>cloud or obfuscate your ability to identify needed SEASONAL ARIMA
>structure.
>
>Foe more on time series please see <a
href="http://www.autobox.com">http://www.autobox.com> and to get
>FREE SOFTWARE that will correctly analyze your series see
><a
href="http://www.autobox.com/freef.exe">http://www.autobox.com/freef.exe>
. For some of the limitations of this
>FREEWARE see <a
href="http://www.autobox.com/Freefore-over.htm">http://www.autobox.com/Freefore-over.htm>
>
>If you wish to contact me ...
>dave reilly
>automatic forecasting systems
>215-675-0652