05202016 11:17 AM
Hi,
In the attachement you can find the output of an ARIMA model with 4 parameters (no intercept): AR1, AR7, MA1 & MA7. I calculated the Yt1, Yt7, et1 & et7 by myself & multiplied with the parameter estimates:
This is my equation:
Yt = 0.91689*Yt1 + 0.99625*Yt7  0.734927Et1  0.78277Et7
The issue is now that my outcome is not the same as the outcome sas provides. For the first 10 observations however I have the same result, both afterwards I have a big difference.
Can anyone help me understanding the difference?
Kind regards,
Olivier
05202016 05:16 PM
AR((1) (7)) = (1  ar1*B)(1  ar7*B**7)Yt
= (1  ar1*B  ar7*B**7 + ar1*ar7*B**8)Yt
= Yt  ar1*Yt1  ar7*Yt7 + ar1*ar7*Yt8
Same applies to MA. So the equation should be
Yt = 0.91689*Yt1 + 0.99625*Yt7 (0.91689 * 0.99625)*Yt8
 0.734927Et1  0.78277Et7 +(0.734927 * 0.78277)*Et8
05202016 02:17 PM
Could you take a look at the Modeling View table and see the exact ARIMA specification for this model? Also what is the interval for t? It goes from 1 to 838 and then back to 1 again?
thanks
alex
05202016 03:08 PM
05202016 03:13 PM
Hi Alex,
Below you can find a printscreen of the modeling view. I suppose the parameter estimates is what you interests most?
Kind regards,
Olivier
05202016 03:42 PM
It looks like the forecast server is picking a factored ARIMA models. For example, P((1)(7)) = (1ar1*B)*(1ar7*B**7), not (1ar1*B  ar7*B**7).
Below is some more info about the factored ARIMA models.
Subset, Seasonal, and Factored ARMA Models
A factored model (also referred to as a multiplicative model) represents the ARIMA model as a product of simpler ARIMA models. For example, you might model SALES
as a combination of an AR(1) process that reflects short term dependencies and an AR(12) model that reflects the seasonal pattern.
It might seem that the way to do this is with the option P=(1 12), but the AR(1) process also operates in past years; you really need autoregressive parameters at lags 1, 12, and 13. You can specify a subset model with separate parameters at these lags, or you can specify a factored model that represents the model as the product of an AR(1) model and an AR(12) model. Consider the following two ESTIMATE statements:
identify var=sales; estimate p=(1 12 13); estimate p=(1)(12);
The mathematical form of the autoregressive models produced by these two specifications are shown in Table 8.2.
Table 8.2: Subset versus Factored Models
Option 
Autoregressive Operator 

P=(1 12 13) 

P=(1)(12) 

Both models fit by these two ESTIMATE statements predict SALES
from its values 1, 12, and 13 periods ago, but they use different parameterizations. The first model has three parameters, whose meanings may be hard to interpret.
The factored specification P=(1)(12) represents the model as the product of two different AR models. It has only two parameters: one that corresponds to recent effects and one that represents seasonal effects. Thus the factored model is more parsimonious, and its parameter estimates are more clearly interpretable.
05202016 03:48 PM
05202016 05:16 PM
AR((1) (7)) = (1  ar1*B)(1  ar7*B**7)Yt
= (1  ar1*B  ar7*B**7 + ar1*ar7*B**8)Yt
= Yt  ar1*Yt1  ar7*Yt7 + ar1*ar7*Yt8
Same applies to MA. So the equation should be
Yt = 0.91689*Yt1 + 0.99625*Yt7 (0.91689 * 0.99625)*Yt8
 0.734927Et1  0.78277Et7 +(0.734927 * 0.78277)*Et8
05202016 05:41 PM
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