An Intervention Model for Ozone Data
/*--------------------------------------------------------------
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;
run;