// --+ 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(structural, model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);

// Define a VAR_EXPECTATION_MODEL
var_expectation_model(model_name = varexp, expression = diff(log(x)), auxiliary_model_name = toto, horizon = 1, discount = beta)  ;

model;
[ name = 'X' ]
diff(log(x)) = b*diff(z) + a*diff(log(x(-1))) + b*(1-a)*diff(log(x(-2))) + c*diff(z(-2)) + e_x;
[ name = 'Z' ]
diff(z) = .1 + f*(diff(z(-1))-diff(log(x)))+c*diff(z(-2)) + e_z;
[ name = 'Y' ]
log(y) = diff(log(x)) + d*log(y(-2)) + e*diff(z(-1)) + e_y;

foo = var_expectation(varexp);
end;

% Evaluate strutural VAR matrices
[ar, a0, const] = example1.varmatrices('toto', M_.params);

assert(isequal(diag(a0), ones(3,1)), 'Diagonal of a0 is wrong.')

assert(a0(1,3)==-b, 'Element (1,3) in A0 is wrong.')
assert(a0(1,2)==0, 'Element (1,2) in A0 is wrong.')
assert(a0(2,1)==-1, 'Element (2,1) in A0 is wrong.')
assert(a0(2,3)==0, 'Element (2,3) in A0 is wrong.')
assert(a0(3,1)==f, 'Element (3,1) in A0 is wrong.')
assert(a0(3,2)==0, 'Element (3,1) in A0 is wrong.')

assert(isequal(ar(:,:,1), [a 0 0; 0 0 e; 0 0 f]), 'First autoregressive matrix is wrong')
assert(isequal(ar(:,:,2), [(1-a)*b 0 c; 0 d 0; 0 0 c]), 'Second autoregressive matrix is wrong')

assert(isequal(const, [.0;.0;.1]), 'Constant vector is wrong.')

% Evaluate reduced form VAR matrices
[AR, ~, CONST] = example1.varmatrices('toto', M_.params, true);

assert(all(all(abs(AR(:,:,1)-a0\ar(:,:,1))<1e-9)), 'Reduced form is wrong (first lag)')
assert(all(all(abs(AR(:,:,2)-a0\ar(:,:,2))<1e-9)), 'Reduced form is wrong (second lag)')
assert(all(abs(CONST-a0\const)<1e-9), 'Reduced form is wrong (constant)')

% Test get_companion_matrix when the VAR model has a constant.
get_companion_matrix('toto', 'var');

assert(all(all(abs(oo_.var.toto.CompanionMatrix-[1, zeros(1, 6); CONST, AR(:,:,1), AR(:,:,2); zeros(3,1), eye(3), zeros(3)])<1e-9)), 'Companion matrix is wrong')