78 lines
2.5 KiB
Modula-2
78 lines
2.5 KiB
Modula-2
// --+ options: stochastic,json=compute +--
|
|
|
|
var foo z x y;
|
|
varexo e_x e_y e_z;
|
|
parameters a b c d e f beta ;
|
|
|
|
a = .9;
|
|
b = -.2;
|
|
c = .3;
|
|
f = .8;
|
|
d = .5;
|
|
e = .4;
|
|
|
|
beta = 1/(1+.02);
|
|
|
|
// Define a VAR model from a subset of equations in the model block.
|
|
var_model(model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
|
|
|
|
/* Define a VAR_EXPECTATION_MODEL
|
|
** ------------------------------
|
|
**
|
|
** model_name: the name of the VAR_EXPECTATION_MODEL (mandatory).
|
|
** var_model_name: the name of the VAR model used for the expectations (mandatory).
|
|
** variable: the name of the variable to be forecasted (mandatory).
|
|
** horizon: the horizon forecast (mandatory).
|
|
** discount: the discount factor, which can be a value or a declared parameter (default is 1.0, no discounting).
|
|
**
|
|
**
|
|
** The `horizon` parameter can be an integer in which case the (discounted) `horizon` step ahead forecast
|
|
** is computed using the VAR model `var_model_name`. Alternatively, `horizon` can be a range. In this case
|
|
** VAR_EXPECTATION_MODEL returns a discounted sum of expected values. If `horizon` is set equal to the range
|
|
** 0:Inf, then VAR_EXPECTATION_MODEL computes:
|
|
**
|
|
** ∑ βʰ Eₜ[yₜ₊ₕ]
|
|
**
|
|
** where the sum is over h=0,…,∞ and the conditional expectations are computed with VAR model `var_model_name`.
|
|
*/
|
|
|
|
var_expectation_model(model_name = varexp, expression = x, auxiliary_model_name = toto, horizon = 0:500, discount = beta) ;
|
|
|
|
|
|
model;
|
|
[ name = 'X' ]
|
|
x = a*x(-1) + b*x(-2) + c*z(-2) + e_x;
|
|
[ name = 'Z' ]
|
|
z = f*z(-1) + e_z;
|
|
[ name = 'Y' ]
|
|
y = d*y(-2) + e*z(-1) + e_y;
|
|
|
|
foo = .5*foo(-1) + var_expectation(varexp);
|
|
end;
|
|
|
|
// Initialize the VAR expectation model, will build the companion matrix of the VAR.
|
|
var_expectation.initialize('varexp')
|
|
|
|
// Update VAR_EXPECTATION reduced form parameters
|
|
var_expectation.update('varexp');
|
|
|
|
/*
|
|
** REMARK The VAR model is such that x depends on past values of x
|
|
** (xₜ₋₁ and xₜ₋₂) and on zₜ₋₂. Consequently the reduced
|
|
** form parameters associated to yₜ₋₁, yₜ₋₂ have to be zero.
|
|
*/
|
|
|
|
weights = M_.params(M_.var_expectation.varexp.param_indices);
|
|
|
|
if weights(3) || ~weights(4) || weights(6) || ~weights(2) || ~weights(5) || ~weights(7) || weights(1)
|
|
error('Wrong reduced form parameter for VAR_EXPECTATION_MODEL')
|
|
end
|
|
|
|
WEIGHTS = load('../3/weights.mat');
|
|
|
|
if max(abs(weights-WEIGHTS.weights))>1e-12
|
|
error('Inconsistent results in var-expectations/3 and var-expectations/4.')
|
|
end
|
|
|
|
delete('../3/weights.mat')
|