*
* Realizations of AR(1) processes from page 55.
*
* Note that these use random numbers. They won't match
* the graphs in the text. If you want to be able to get
* your own graphs to match from one run to another, use
* the SEED instruction at the top of the program. The syntax
* for this is SEED big integer, like SEED 53435. RATS (like
* almost all software) can only generate "pseudo-random"
* numbers. These are generated systematically from a seed value,
* but pass virtually any test for randomness. From a fixed
* seed, you will always get the same numbers.
*
all 100
*
* The AR(1) processes use the "FIRST" option on SET to choose
* a different formula for the initial data point, since it
* doesn't have a lag for the recursive definition. This is
* a draw from the unconditional distribution, see 3.4.4 for
* the calculation of the unconditional variance of an AR(1)
* process.
*
set ywn = %ran(1.0)
set(first=%ran(1.0)/(1-.5**2)) y5 = .5*y5{1}+%ran(1.0)
set(first=%ran(1.0)/(1-.9**2)) y9 = .9*y9{1}+%ran(1.0)
grparm(font=symbol) hlabel 24
spgraph(vfields=3,header='Figure 3.3 Realizations of an AR(1) Process')
graph(hlabel='f=0')
# ywn
graph(hlabel='f=0.5')
# y5
graph(hlabel='f=0.9')
# y9
spgraph(done)