Grocer Function
NAME
arma2param - explodes a Varmax model for estimation uses
CALLING SEQUENCE
[theta,theta2mat,V2theta,thetalab,AR,ARS,MA,MAS,G,V,p,P,q,Q,g,s,k,n,np,%type,vdiag,ineq]=arma2param(m,AR,ARS,MA,MAS,V,s,G,r,namexos)
PARAMETERS
Input
-
m = # of endogenous variables
-
AR = a string, representing the name of the AR part of the model
-
ARS = a string, representing the name of the seasonal AR part of the model
-
MA = a string, representing the name of the MA part of the model
-
MAS = a string, representing the name of the seasonal MA part of the model
the names of FR, FS, AR and AS represent objects that can
be either of constant type or list type; in the last case, the first item of the list should represent as in the fist case the starting value of the corresponding matrix, and second one a string matrix, of same size, of constraints ('' for no constraint, '=' for equality constraint, 'value< *', '*< value' or 'value1< *< value2' for inequality constraints)
- V = a (mxm) (var-covar) matrix or a (mx1) vector (the diagonal of a var-covar matrix,
supposed to have 0 outside the diagonal)
-
s = order of seasonality
-
G = the coefficients martrix for the endogenous variables (if any)
-
r = # of exogenous variables (if any)
Output
-
theta = (npx1) vector of parameters that will be estimated
-
theta2mat = vector of strings, representing the instructions that transform back theta into the input parameters
-
V2theta = vector of strings, representing the instructions
that transform V into the corresponding parameters in theta thetalab = (npx1) vector of strings, representing theta names used when printing the results
-
FR = the AR part of the model
-
FS = the seasonal AR part of the model
-
AR = the MA part of the model
-
AS = the seasonal MA part of the model
-
G = the coefficients matrix for the endogenous variables
- V = the (mxm) (var-covar) matrix
-
p = degree of the AR part of the model
-
P = degree of the seasonal AR part of the model
-
q = degree of the MA part of the model
-
Q = degree of the seasonal MA part of the model
-
s = order of seasonality
-
k = maximum degree of the total AR, MA and G parts
-
n = k*m
-
np = # of estimated parameters
-
%type = type of the e4 model
-
vdiag = 0 if V is diagonal, 1 if not
DESCRIPTION
arma2param - explodes a Varmax model for estimation uses The input arguments corresponding to the model:
(I + AR1·B + ... +ARp·B^p)(I + ARS1·B^s + ... + ARSps·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) e(t)
are:
AR = [AR1 | ... | ARp] ARS = [ARS1 | ... | ARSps]
G = [G0 | G1 | ... | Gg] MA = [MA1 | ... | MAq] MAS = [MAS1 | ... | MASqs]
EXAMPLE
1.
[theta,grocer_e4_theta2mat,grocer_e4_V2theta,grocer_e4_lab,grocer_AR,grocer_ARS,grocer_MA,grocer_MAS,G,grocer_V,...
grocer_e4_p,grocer_e4_P,grocer_e4_q,grocer_e4_Q,grocer_e4_g,...
grocer_e4_s,grocer_e4_k,grocer_e4_n,grocer_e4_np,grocer_e4_type,grocer_e4_vdiag,grocer_e4_ineq] ...
= arma2param(grocer_e4_m,grocer_AR,grocer_ARS,grocer_MA,grocer_MAS,...
grocer_v,grocer_s,grocer_e4_Gexo,grocer_e4_r,grocer_e4_namexo);
2.
[theta,grocer_e4_theta2mat,grocer_e4_V2theta,grocer_e4_lab,grocer_AR,grocer_ARS,grocer_MA,grocer_MAS,G,grocer_V,...
grocer_e4_p,grocer_e4_P,grocer_e4_q,grocer_e4_Q,grocer_e4_g,...
grocer_e4_s,grocer_e4_k,grocer_e4_n,grocer_e4_np,grocer_e4_type,grocer_e4_vdiag,grocer_e4_ineq] ...
= arma2param(grocer_e4_m,grocer_AR,grocer_ARS,grocer_MA,grocer_MAS,grocer_v,grocer_s);
Both examples taken from function varma(); the first example deals with the case when there are exogenous variables
(for instance a constant), the second one when there are no exogenous variables (in particular no constant).
AUTHOR
Eric Dubois 2004