Turn on suggestions

Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

- Home
- /
- Analytics
- /
- Forecasting
- /
- What is the mathematical form of an ARIMA forecast?

Options

- RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Mute
- Printer Friendly Page

🔒 This topic is **solved** and **locked**.
Need further help from the community? Please
sign in and ask a **new** question.

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Posted 03-14-2011 08:11 AM
(6428 views)

I created an ARIMA model in SAS, but I need to implement the formula

for the forecasts in Excel. Below is the SAS code for the model. The model is

AR(5,10,15,20) MA(1,5) with differencing of 5 periods.

proc arima data=test;

identify var=calls (5) nlag=49;

estimate p=(5 10 15 20) q=(1 5);

run;

I tried using Y(t)-Y(t-5)=Mu+MA/AR, but the forecasts on the spreadsheet are still different from the SAS output. This notation is based on a document from SAS Support here: http://support.sas.com/documentation/cdl/en/etsug/60372/HTML/default/viewer.htm#etsug_tffordet_sect0...

Can you please help me with translating the ARIMA forecast to Excel? Thank you.

Valentin

for the forecasts in Excel. Below is the SAS code for the model. The model is

AR(5,10,15,20) MA(1,5) with differencing of 5 periods.

proc arima data=test;

identify var=calls (5) nlag=49;

estimate p=(5 10 15 20) q=(1 5);

run;

I tried using Y(t)-Y(t-5)=Mu+MA/AR, but the forecasts on the spreadsheet are still different from the SAS output. This notation is based on a document from SAS Support here: http://support.sas.com/documentation/cdl/en/etsug/60372/HTML/default/viewer.htm#etsug_tffordet_sect0...

Can you please help me with translating the ARIMA forecast to Excel? Thank you.

Valentin

1 ACCEPTED SOLUTION

Accepted Solutions

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

This is not the answer you are looking for, but in my opinion you will have a hard time replicating ARIMA models created in SAS using Excel. The implementation of these kinds of models is more sophisticated than you might expect - and as such difficult to translate to simple Excel statements (in a straightforward manner that is).

Wouldn't it be more appropriate to leave the calculation of the ARIMA model in SAS and export the results to Excel only?

Thanks,

Udo

5 REPLIES 5

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

This is not the answer you are looking for, but in my opinion you will have a hard time replicating ARIMA models created in SAS using Excel. The implementation of these kinds of models is more sophisticated than you might expect - and as such difficult to translate to simple Excel statements (in a straightforward manner that is).

Wouldn't it be more appropriate to leave the calculation of the ARIMA model in SAS and export the results to Excel only?

Thanks,

Udo

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

i have tried replicating the SAS ARIMA (AR model) model in excel and have been successful for the most part... below is the equation that i am using..

below is the equation for p =(1,7,14) model with no d and q terms

Yt = Constant Estimate + ar1*lag1 +ar7*lag7 +ar14*lag14

if the model has other input variables apart from these 3 lags, below is the equation (p =(1,7,14), with input=Temp, with no d and q terms):

Yt = Constant Estimate + ar1*lag1 +ar7*lag7 +ar14*lag14+ num1*Temp-ar1*num1*temp1-ar7*num1*temp7-ar14*num1*temp14

hope this helps.

thanks

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Thanks for the Logic, I am struggling with the notations num1. Can you please clarify?

Thanks in advance!

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

num1,num2 etc. are coefficients for other terms you may include in your arima model.. proc arima lets you add other variables (like regressive) into your model using the followin statement:

estimate input=XYZ;

referrence: http://support.sas.com/documentation/cdl/en/etsug/63348/HTML/default/viewer.htm#etsug_arima_sect012....

hope that helps... if you just have AR term you don't have to worry about the num1,num2 etc.

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Thanks for the quick response. It helped me move 1 step ahead, I could replicate ARMA (1,1) with 2 input variables. Now I am trying extend it to a general form of more than 1 AR term (AR 1,2 ) with 2 or more input variables. The below mentioned form does not conform with SAS output.

Yt = Constant Estimate + ar1*lag1 +ar2*lag2 + num1*Temp-ar1*num1*Temp1-ar2*num1*Temp2 {changed the subscripts}

Yt = Constant Estimate + ar1*lag1 +ar2*lag2 + num1*(Temp- ar1*Temp1- ar2*Temp2) {brought num1 forward}

Yt = Constant Estimate + ar1*lag1 +ar2*lag2 + num1*(Temp- (ar1*Temp1+ ar2*Temp2)) {Regression - AR contribution to get the marginal contribution for temp}

I believe the above form suggests that whenever you have AR with input variables, we need to take out the AR interaction out of the input variable to see the marginal contribution of the input variable (Temp in our case). This form does not match with SAS

So i think, there should be a term to take care of the effect of interaction between Ar1 and Ar2 something like A1*Ar2

Yt = Constant Estimate + ar1*lag1 +ar2*lag2 + num1*(Temp-(ar1*temp1 + ar2*temp2 - ar1*temp1*ar2*temp2)

Unfortunately this does not help either.

Nav1, any guidance would be helpful. Thanks a ton!

**SAS Innovate 2025** is scheduled for May 6-9 in Orlando, FL. Sign up to be **first to learn** about the agenda and registration!

Multiple Linear Regression in SAS

Learn how to run multiple linear regression models with and without interactions, presented by SAS user Alex Chaplin.

Find more tutorials on the SAS Users YouTube channel.