options ls=72; 
 /*-----------------------------------------------------------
 |  Data from Shipping Liu.  Sales of milk in Hawaii.  In April |
 |  of '82 news of milk contamination was released.  Sales fell |
 |  and bottomed out in May then returned toward the previous   |
 |  level slowly.                                               |
 |____________________________________________________________*/

data liu; input dddd $ sales;
retain date '01jan77'd; date=intnx('month',date,1);
label sales = 'Milk Sales';
title 'Effect of Negative Publicity (Contamination)';
title2 'on Milk Sales';
x = (date='01apr82'd);
x2 = (date>'01mar82'd);  ** check for permanent shift **;
format date monyy.;
    if _n_=1 then do; Plag=0; Xlag=0; end;
    P =  - 3167440*X - 4855974*xlag + .56562*Plag ;
    YHAT = 8674594 + P -1079129*x2;
    output; retain; Plag=P ; xlag=x;
cards;
    FEB77    9331400
    MAR77    8366100
    APR77    9357500
    MAY77    8674600
    JUN77    9106200
    JUL77    7522500
    AUG77    7797800
    SEP77    7980700
    OCT77    9436400
    NOV77    9170500
    DEC77    9060600
    JAN78    8414700
    FEB78    9207000
    MAR78    8124600
    APR78    9216900
    MAY78    9310700
    JUN78    9406200
    JUL78    8004100
    AUG78    8062200
    SEP78    8322100
    OCT78    9353400
    NOV78    9432600
    DEC78    9060100
    JAN79    9041600
    FEB79    9385200
    MAR79    8666200
    APR79    9721700
    MAY79    9416400
    JUN79    9523700
    JUL79    8601100
    AUG79    8442400
    SEP79    8583800
    OCT79    8883600
    NOV79    9076300
    DEC79    8267200
    JAN80    9248300
    FEB80    9470800
    MAR80    9289600
    APR80    9563500
    MAY80    9462900
    JUN80    9603800
    JUL80    8216000
    AUG80    8413300
    SEP80    8525200
    OCT80    9012400
    NOV80    9297300
    DEC80    8717500
    JAN81    8524000
    FEB81    9212700
    MAR81    8415200
    APR81    8565100
    MAY81    9164100
    JUN81    9293100
    JUL81    7892100
    AUG81    8345700
    SEP81    8249400
    OCT81    8884000
    NOV81    8938400
    DEC81    8186200
    JAN82    8265100
    FEB82    8483400
    MAR82    7768100
    APR82    4443700
    MAY82    1460800
    JUN82    4119000
    JUL82    5342600
    AUG82    5913000
    SEP82    6098000
    OCT82    6587700
    NOV82    7344500
    DEC82    7081900
    JAN83    7199700
    FEB83    7642900
    MAR83    6960400
    APR83    8446100
    MAY83    8075100
    JUN83    8367600
    JUL83    6906300
    ;
  * Plot the data ;
proc print;
proc gplot;
   plot YHAT*date sales*date / overlay href = '01apr82'd;
   symbol1 v=none i=join c=red w=2; 
   symbol2 v=dot c=blue h=1.5; 



  *  Check ARIMA structure using pre-intervention data;

proc arima; identify var=sales; where date < '01apr82'd;
e p=(1,2)(12) ml;
e p=(1)(12) q=(2) ml;

  *  Fit intervention model.  MA term allows 2 successive dropoffs before
     recovery ;

proc arima; identify var=sales noprint crosscor=(x x2);
 e input=( (1) /(1) x x2) p=(1)(12) q=(2) ml;

run;