*
* ACF's of generated series
*
all 250
*
* The unconditional distribution of the AR(1) process is y(t)~N(0,4.0/(1-.7**2)).
* We use SET with the FIRST option to draw the first value from the unconditional
* density; then the others are created by applying the conditional model. Note
* that the RATS %ran function (which draws independent normals) takes the
* standard deviation as the argument, not the variance.
*
* Note that because this is based upon (pseudo) random numbers, the output will
* not match that shown in the text. If you want a RATS program to generate the
* same "random" numbers each time, you can use the SEED instruction. The syntax
* of this is SEED big integer. For instance, if you take the comment * off the
* front of the next instruction, you'll get the same results each time you run
* this program.
*
*SEED 950343
set(first=%ran(sqrt(4.0/(1-.7**2)))) y = .7*y{1}+%ran(2.0)
graph(footer="Figure 14.3 AR(1) Process with rho=.7")
# y
@bjident(number=12,method=yule,qstats,report) y
*
* An MA(1) process is also fairly easy to create. You generate a series of
* shocks, then create a second series from the moving average of that one. Again,
* we use SET with the FIRST option to take care of the first observation, which
* can't be computed using the standard formula because there is no lagged value
* of u available.
*
set u = %ran(2.0)
set(first=u(1)+.4*%ran(2.0)) x = u+.4*u{1}
graph(footer="Figure 14.5 MA(1) Process with theta=.4")
# x
@bjident(number=12,method=yule,qstats,report) x