On Mon, 26 Mar 2012, Riccardo (Jack) Lucchetti wrote:
So you end up with an estimate of the coefficients for the MA
polynomial whose inverse roots are
-1.2736
-0.40100 + 0.93150i
-0.40100 - 0.93150i
0.63538 + 0.36511i
0.63538 - 0.36511i
Ooof, I really should read my own messages before sending them. These are
the _roots_, not the inverse roots. However, my point still stands (the MA
polynomial is nonivertible). To make amends, I'll include a short hansl
script that someone may find useful/instructive/fun to look at
<hansl>
set echo off
set messages off
#estimated MA coefficients
c = {-0.804878, 0.0506545, 0.180421, 0.563758, -0.703441}
matrix T = c | (I(4) ~ 0)
l = eigengen(T)
il = cdiv(ones(5,1), l)
m = sqrt(sumr(l.^2))
printf " Roots Inverse Roots Modulus\n\n"
loop i=1..rows(l) --quiet
scalar x = il[i,2]
if x>0
printf "%9.6f + %9.6fi,", il[i,1], x
elif x<0
printf "%9.6f - %9.6fi,", il[i,1], abs(x)
else
printf "%9.6f ,", il[i,1]
endif
scalar x = l[i,2]
if x>0
printf " %9.6f + %9.6fi", l[i,1], x
elif x<0
printf " %9.6f - %9.6fi", l[i,1], abs(x)
else
printf " %9.6f ", l[i,1]
endif
printf ", %9.6f\n", m[i]
endloop
</hansl>
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti