*
* Constructed examples of recursive analysis, pp 235-238
* Note that these all depend upon random numbers, and so will not match (exactly)
* the results in the textbook, and won't match even from one run to the next. If
* you want to be able to reproduce exactly a set of results, add the instruction
*
*    SEED  big integer   (like SEED 534653) at the top of the program.
*
all 200
set x = (t)
set y1 = .5*x+%ran(10.0)
spgraph(hfields=2,vfields=2,footer="Figure 9.15 Recursive Analysis: Constant Parameter Model")
scatter
# x y1
compute startr=3,end=200
rls(cohist=cohist,sehist=sehist,sighist=sighist,csum=cusum) y1 / resids
# x
set upperco = cohist(1)+sehist(1)*2.0
set lowerco = cohist(1)-sehist(1)*2.0
graph(header="Recursive Estimates") 3
# cohist(1)
# upperco 10 * 2
# lowerco 10 * 2
set upperres =  2.0*sighist
set lowerres = -2.0*sighist
graph(header="Recursive Residuals") 3
# resids
# upperres / 2
# lowerres / 2
set cusum = cusum/sqrt(%seesq)
set upper5 startr end = .948*sqrt(%ndf)*(1+2.0*(t-startr)/%ndf)
set lower5 startr end = -upper5
graph(header="CUSUM test") 3
# cusum
# upper5 / 2
# lower5 / 2
spgraph(done)
*
set y2 = (.02*t)*x+%ran(10.0)
spgraph(hfields=2,vfields=2,footer="Figure 9.16 Recursive Analysis: Trending Parameter Model")
scatter
# x y2
rls(cohist=cohist,sehist=sehist,sighist=sighist,csum=cusum) y2 / resids
# x
set upperco = cohist(1)+sehist(1)*2.0
set lowerco = cohist(1)-sehist(1)*2.0
graph(header="Recursive Estimates") 3
# cohist(1)
# upperco 10 * 2
# lowerco 10 * 2
set upperres =  2.0*sighist
set lowerres = -2.0*sighist
graph(header="Recursive Residuals") 3
# resids
# upperres / 2
# lowerres / 2
set cusum = cusum/sqrt(%seesq)
set upper5 startr end = .948*sqrt(%ndf)*(1+2.0*(t-startr)/%ndf)
set lower5 startr end = -upper5
graph(header="CUSUM test") 3
# cusum
# upper5 / 2
# lower5 / 2
spgraph(done)
*
set y3 = %if(t<=100,x,3*x)+%ran(10.0)
spgraph(hfields=2,vfields=2,footer="Figure 9.17 Recursive Analysis: Breaking Parameter Model")
scatter
# x y3
rls(cohist=cohist,sehist=sehist,sighist=sighist,csum=cusum) y3 / resids
# x
set upperco = cohist(1)+sehist(1)*2.0
set lowerco = cohist(1)-sehist(1)*2.0
graph(header="Recursive Estimates") 3
# cohist(1)
# upperco 10 * 2
# lowerco 10 * 2
set upperres = 2.0*sighist
set lowerres = -2.0*sighist
graph(header="Recursive Residuals") 3
# resids
# upperres / 2
# lowerres / 2
set cusum = cusum/sqrt(%seesq)
set upper5 startr end = .948*sqrt(%ndf)*(1+2.0*(t-startr)/%ndf)
set lower5 startr end = -upper5
graph(header="CUSUM test") 3
# cusum
# upper5 / 2
# lower5 / 2
spgraph(done)