*
* Autocorrelations from page 38
*
calendar(q) 1947:2
*
open data ch02_usgnp_q(47-91).txt
data(format=free,org=columns) 1947:2 1991:1 rgnp
*
spgraph(vfields=1,footer="Figure 2.5 Time Plot of US Quarterly Real GNP")
graph(vlabel="growth")
# rgnp
spgraph(done)
*
linreg rgnp
# constant rgnp{1 2 3}
*
* %EQNLAGPOLY extracts the lag polynomial from an equation or (if its first
* argument is zero) from the last run regression. The second argument is the
* variable whose lag polynomial is extracted. Because ggnp is the dependent
* variable in the equation, you get the left side polynomial in the third-order
* difference equation on page 34. %POLYCXROOTS then computes the roots of that
* polynomial. Since we don't know which will be the complex roots (if there are
* any), we need to display them before the next step. (The roots are ordered by
* their absolute values)
*
compute croots=%polycxroots(%eqnlagpoly(0,rgnp))
disp croots
*
* The 2nd and 3rd roots are complex. The cycle length can be obtained by the
* following - the %arg function returns the inverse tangent (in radians) of b/a
* for the complex number a+bi. We'll work with the 2nd root, since it will give a
* positive value for the cycle length. The 3rd root will give the negative of
* this value.
*
disp "Average Length of Cycles" 2*%pi/%arg(croots(2))