# st: time series simulation study

 From "Sascha O. Becker" <[email protected]> To [email protected] Subject st: time series simulation study Date Tue, 6 May 2003 12:11:44 +0200 (MEST)

```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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```