<< pacf ARMA and VARMA tools theta2arma >>

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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

load(GROCERDIR+'/data/varma_d.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

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