/* Spurious Regression Simulation */

/* Compare Regressions on Levels versus Differences */

/* Simulate Independent Random Walks */

/* Tom Fomby, Dept. of Economics, SMU, Dallas, TX 75275 */

/* References:

	Granger, C., and P. Newbold (1974), "Spurious Regressions in Econometrics,"
    Journal of Econometrics, 2, 111-120.

    Phillips, P. (1986), "Understanding Spurious Regressions," Journal of
    Econometrics, 33, 311-340.

*/

data rw;
seedy=123456;
seedx=654321;
do sample = 1 to 20;
 y =0;
 x =0;
  do time = 1 to 1000;
  y = y;
  x = x;
  y = 0.00 + y + rannor(seedy);
  x = 0.00 + x + rannor(seedx);
  dy = y - lag(y);
  dx = x - lag(x);
 if time > 500 then output;
 end;
end;
run;

/* run regressions by sample */

proc reg data=rw;
model y = x;
model dy = dx;
by sample;
run;