Grocer Function
NAME
theta2arm2 - transformation of VARMA estimate into the corresponding matrices
CALLING SEQUENCE
[AR,ARS,MA,MAS,V,G]=theta2arm2(theta,theta2mat,fromgrad)
PARAMETERS
Input
-
theta = (npx1) vector of parameters
-
theta2mat = a string vector of instructions that transforms
-
fromgrad = if not given, forces the matrix V to be positive definite
Output
-
AR,AS,MA,MAS,V,G = matrices of the process:
(I + AR1·B +...+ARp·B^p)(I + AS1·B^s +...+ ASps·B^ps·s) y(t)
= (G0 + G1·B +...+ Gt·B^l) u(t) +
(I + MA1·B +...+MAq·B^q)(I + MAS1·B^s +...+ MASqs·B^qs·s) a(t)
with Var(a(t)) = V
DESCRIPTION
Recovers the matrices of an ARMA process from the values of the estimated parameters.
EXAMPLE
mtlb_load('SCI/scied/grocer/encours/e4sci/seriesa.dat'); elec_cons = transdif(seriesa,0,1,1,12);
results=varma(elec_cons,[],[],0,0,0,12); grocer_AR=[];grocer_ARS=[];grocer_MA=[];grocer_MAS=[];grocer_V=[];grocer_G[];
[AR,ARS,MA,MAS,V,G]=theta2arm2(results('coeff'),results('theta2mat'),1)
Although theta2arm2 is mainly useful for the estimation of a VARMA model, this example shows how it can be used to recover
the estimated matrices from the tlist results produced by the function VARMA. Note however that it imposes to
define the matrices grocer_AR,..., grocer_G; so this capability should be used with care...
AUTHOR
Jaime Terceiro, 1997/ Eric Dubois 2004