Ok. Thanks for point it out. My goal is not forecasting for the future months with historical data. I expected to build a A/B test and have no idea on how to define a control and a test group. Not clear on how to implement the example below to design A/B test. Not sure if comparing the results with X1 and without X1 by running the ARIMA model below twice. Could anyone shed some light on it? Thanks, Here is the time series data and ARIMA code: /*--------------------------------------------------------------
SAS Sample Library
Name: ariex04.sas
Description: Example program from SAS/ETS User's Guide,
The ARIMA Procedure
Title: An Intervention Model for Ozone Data
Product: SAS/ETS Software
Keys: time series analysis
PROC: ARIMA
Notes:
--------------------------------------------------------------*/
title1 'Intervention Data for Ozone Concentration';
title2 '(Box and Tiao, JASA 1975 P.70)';
data air;
input ozone @@;
label ozone = 'Ozone Concentration'
x1 = 'Intervention for post 1960 period'
summer = 'Summer Months Intervention'
winter = 'Winter Months Intervention';
date = intnx( 'month', '31dec1954'd, _n_ );
format date monyy.;
month = month( date );
year = year( date );
x1 = year >= 1960;
summer = ( 5 < month < 11 ) * ( year > 1965 );
winter = ( year > 1965 ) - summer;
datalines;
2.7 2.0 3.6 5.0 6.5 6.1 5.9 5.0 6.4 7.4 8.2 3.9
4.1 4.5 5.5 3.8 4.8 5.6 6.3 5.9 8.7 5.3 5.7 5.7
3.0 3.4 4.9 4.5 4.0 5.7 6.3 7.1 8.0 5.2 5.0 4.7
3.7 3.1 2.5 4.0 4.1 4.6 4.4 4.2 5.1 4.6 4.4 4.0
2.9 2.4 4.7 5.1 4.0 7.5 7.7 6.3 5.3 5.7 4.8 2.7
1.7 2.0 3.4 4.0 4.3 5.0 5.5 5.0 5.4 3.8 2.4 2.0
2.2 2.5 2.6 3.3 2.9 4.3 4.2 4.2 3.9 3.9 2.5 2.2
2.4 1.9 2.1 4.5 3.3 3.4 4.1 5.7 4.8 5.0 2.8 2.9
1.7 3.2 2.7 3.0 3.4 3.8 5.0 4.8 4.9 3.5 2.5 2.4
1.6 2.3 2.5 3.1 3.5 4.5 5.7 5.0 4.6 4.8 2.1 1.4
2.1 2.9 2.7 4.2 3.9 4.1 4.6 5.8 4.4 6.1 3.5 1.9
1.8 1.9 3.7 4.4 3.8 5.6 5.7 5.1 5.6 4.8 2.5 1.5
1.8 2.5 2.6 1.8 3.7 3.7 4.9 5.1 3.7 5.4 3.0 1.8
2.1 2.6 2.8 3.2 3.5 3.5 4.9 4.2 4.7 3.7 3.2 1.8
2.0 1.7 2.8 3.2 4.4 3.4 3.9 5.5 3.8 3.2 2.3 2.2
1.3 2.3 2.7 3.3 3.7 3.0 3.8 4.7 4.6 2.9 1.7 1.3
1.8 2.0 2.2 3.0 2.4 3.5 3.5 3.3 2.7 2.5 1.6 1.2
1.5 2.0 3.1 3.0 3.5 3.4 4.0 3.8 3.1 2.1 1.6 1.3
. . . . . . . . . . . .
;
proc arima data=air;
/* Identify and seasonally difference ozone series */
identify var=ozone(12)
crosscorr=( x1(12) summer winter ) noprint;
/* Fit a multiple regression with a seasonal MA model */
/* by the maximum likelihood method */
estimate q=(1)(12) input=( x1 summer winter )
noconstant method=ml;
/* Forecast */
forecast lead=12 id=date interval=month out=arimaout;
run;
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