Different results from Proc arima and proc autoreg

[sasalex2024]

Dear SAS Community,

I am working with a dataset (please see below) and attempting to run a model with one AR and two MA terms. However, I’ve noticed a significant discrepancy between the results generated by PROC ARIMA and PROC AUTOREG. Below are the codes I used:

proc autoreg data=a;
model consump = consumplag / method=ml nlag=2;
run;

vs

proc arima data=a;
   identify var=consump;
   estimate p=1 q=2 method=ml;
run;

Any insights into why these two procedures are producing different results would be greatly appreciated. The data are shown below:

yr	consump	consumplag
1920	39.8
1921	41.9	39.8
1922	45	41.9
1923	49.2	45
1924	50.6	49.2
1925	52.6	50.6
1926	55.1	52.6
1927	56.2	55.1
1928	57.3	56.2
1929	57.8	57.3
1930	55	57.8
1931	50.9	55
1932	45.6	50.9
1933	46.5	45.6
1934	48.7	46.5
1935	51.3	48.7
1936	57.7	51.3
1937	58.7	57.7
1938	57.5	58.7
1939	61.6	57.5
1940	65	61.6
1941	69.7	65

[SASCom1 · Accepted solution]

Hello @sasalex2024 

If you wanted to fit a ARMA(1,2)  model, then your PROC ARIMA code is correct. However, PROC AUTOREG does not support MA terms, and you cannot specify ARMA models in PROC AUTOREG. Your PROC AUTOREG is specifying a regression of consump on its own lag, and the error term in this regression follows AR(2) process. Please see the equations for regressions with AR errors specified in PROC AUTOREG:

https://go.documentation.sas.com/doc/en/pgmsascdc/v_055/etsug/etsug_autoreg_gettingstarted01.htm

I hope this helps.