/*Regression with Autocorrelated Errors AR(1)*/

options ls=80;

data a;

e1=0;

do time=-5 to 100;

e=.7*e1+rannor(1234); /* Var(a)=1 */

y=10+.5*time+e;

if time>0 then output;

e1=e;

end;

run;

/*To graph we could use Solutions>Analysis>Time Series Viewer*/

/*Let's ignore Autocorrelation*/

ods html ;

Proc autoreg data=a;

model y=time;

run;

/*Conclusion: OLS overestimates MSE */

Proc autoreg data=a;

model y=time/nlag=1 iter; /*The sample size is OK*/

run;

data future;

input y time;

datalines;

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run;

data a1;

update a future;

by time;

run;

/*A Time Series with AR(1) errors*/

Proc arima data=a1;

identify var=y

crosscor=(time) ;

estimate input=(time) p=(1) printall plot;

forecast lead=12 out=fcast;

run;

proc print data=fcast;

run;

ods html close;