Dear statalisters,
in a simulation study (with something like 1000 replications), I want to
generate simple AR(k) time series
y(t) = c + b0 * t + b1 * y(t-1) + b2* y(t-2) +...+ bk* y(t-k)+ eps.
where I want to pick values t=450, ..., 500, i.e. after the time series has
somewhat stabilised. I.e. I want to generate 1000 time series like this
(using simul "around" the procedure below) .
For the case where b2=...=bk=0, i.e. an AR(1), I can do it pretty easily
using the feature that Stata's "replace" command replaces recursively. What I do
is:
*********************
set seed 1;
set obs 10;
generate mynormal=invnorm(uniform());
g time=_n;
tsset time;
g y=.;
replace y=mynormal in 1; /* use the first entry in mynormal as a y(0) and
the rest as epsilons */
replace y=1+b0*time+b1*l.y+mynormal if time>1; /* NOTE: replace works
recursively !! */
list;
*********************
which yields
list;
mynormal time y
1. .4349075 1 .4349075
2. 1.460773 2 13.0046
3. -.0389092 3 29.03223
4. -.0759261 4 49.95335
5. 1.921223 5 77.76375
6. .1418411 6 108.6329
7. .8990735 7 145.0734
8. .9799716 8 186.3653
9. .2037313 9 231.6133
10. -.3139055 10 281.0451
I do not see immediately how to generate higher order AR(k) (k>1).
Any suggestions?
Best, Sascha
Dr. Sascha O. Becker - Center for Economic Studies
Department of Economics - University of Munich
Schackstr. 4 - 80539 Munich, Germany
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