/* Simulate various types of time series data */
data sim;
call streaminit(123);
do t=1 to 1000;
	e = rand("Normal",0,1);

	/* White noise */
	y_wn = e;

	/* Random walk */
	if t=1 then y_rw = e;
	else y_rw = y_rwl + e; 

	/* Random walk with drift */
	if t=1 then y_drw = e;
	else y_drw = 0.0005*t + y_drwl + e;

	/* Reversion to mean */
	if t=1 then y_rev = e;
	else y_rev = 0.9*y_revl + e;  

	/* Specify time windows */
	if t<300 then period=1;
	else if 300<=t<600 then period=2;
	else period=3;

	output;

	/* Generate lagged values */
	y_rwl = y_rw;
	y_drwl = y_drw;
	y_revl = y_rev;

end;
label y_wn = "White noise"
   	  y_rw = "Random walk"
	  y_drw = "Random walk with drift"
	  y_rev = "Reversion to mean"
	  t = "Time";
run;

/* Generate plots of these variables */
proc sgplot data=sim;
series x=t y=y_wn;
refline 0 / lineattrs=(color=red thickness=4);
run;
proc sgplot data=sim;
series x=t y=y_rw;
refline 0 / lineattrs=(color=red thickness=4);
run;
proc sgplot data=sim;
series x=t y=y_drw;
run;
proc sgplot data=sim;
series x=t y=y_rev;
refline 0 / lineattrs=(color=red thickness=4);
run;

/* Statistical properties */
proc means data=sim mean var;
by period;
var y_wn y_rw y_drw;
run;

/* First difference random walk */
data sim;
set sim;
y_rw_dif = dif(y_rw);
label y_rw_dif = "First-differenced random walk";
run;
proc sgplot data=sim;
series x=t y=y_rw_dif / y2axis;
series x=t y=y_rw / lineattrs=(thickness=3);
refline 0 / lineattrs=(color=red thickness=4);
run;