*
* Examples of ACF's from pages 50-51
*
all 20
*
* These use the procedure EQNTOACF to produce the autocorrelation functions for a
* model. The EQUATION instruction is used to input the models. For this use, we
* use the AR and MA parameters (3rd and 4th) on the EQUATION instruction to set
* the number of AR's and MA's. A constant is added by default - since an
* intercept doesn't matter for our purposes, we use the NOCONSTANT option to
* leave it out. The only exception to this is the white noise equation, which
* wouldn't have any explanatory variables if not for the constant. We put the
* generated autocorrelation functions into five separate series.
*
equation(const,coeffs=||0.0||) arma y 0 0
@eqntoacf(number=20,corrs) arma acfwn
equation(noconst,coeffs=||0.8||) arma y 0 1
@eqntoacf(number=20,corrs) arma acfma1
equation(noconst,coeffs=||-.6,+.3,-.5,+.5||) arma y 0 4
@eqntoacf(number=20,corrs) arma acfma4
equation(noconst,coeffs=||0.8||) arma y 1 0
@eqntoacf(number=20,corrs) arma acfar1
equation(noconst,coeffs=||-.8||) arma y 1 0
@eqntoacf(number=20,corrs) arma acfar1n
*
* Graph the five series in five cells of a 3x2 matrix of graphs. The collection of
* options number=0,min=-1.0,max=1.0,style=bar is the standard set for graphing
* autocorrelations. The point of using min and max is to ensure that the graphs
* have a common range so a given value will have the same height no matter how
* large or small the other correlations are for the same series.
*
grparm(font=helvetica) hlabel 24
spgraph(vfields=3,hfields=2,footer="Figure 3.1 Autocorrelation Functions for Assorted ARMA Processes")
graph(number=0,min=-1.0,max=1.0,style=bar,hlabel="White Noise")
# acfwn
graph(number=0,min=-1.0,max=1.0,style=bar,hlabel="MA(4)")
# acfma4
graph(number=0,min=-1.0,max=1.0,style=bar,hlabel="AR(1) with -.8")
# acfar1n
graph(number=0,min=-1.0,max=1.0,style=bar,hlabel="MA(1)")
# acfma1
graph(number=0,min=-1.0,max=1.0,style=bar,hlabel="AR(1) with .8")
# acfar1
spgraph(done)
*
* This computes and graphs the first lag autocorrelation for the MA(1) process
* y(t)=u(t)+theta*u(t-1) for various values of theta. To get the appearance of a
* continuous curve, the autocorrelations are computed on a fine grid. Here this
* runs from -2.99 to 3.00 by steps of .01. The "q" on the hlabel gets translated
* into a theta in symbol font.
*
grparm(font=symbol) hlabel 24
set theta 1 600 = (t-300)*.01
set corrs 1 600 = theta/(1+theta**2)
scatter(style=lines,vmax=1.0,vmin=-1.0,vgrid=||.5,-.5||,$
  footer="Figure 3.2 First Autocorrelation for an MA(1) Process",hlabel="q")
# theta corrs