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Added example (VECM with double differences).

time-shift
Stéphane Adjemian(Charybdis) 2018-05-31 13:43:26 +02:00
parent 9f00a1573e
commit 1d0a2ae7a3
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// --+ options: json=compute +--
var x1 x2 x1bar x2bar z ;
varexo ex1 ex2 ex1bar ex2bar ez ;
parameters a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
e_c_m c_z_1 c_z_2 gamma beta ;
a_x1_0 = -.9;
a_x1_1 = .4;
a_x1_2 = .3;
a_x1_x2_1 = .1;
a_x1_x2_2 = .2;
a_x2_0 = -.9;
a_x2_1 = .2;
a_x2_2 = -.1;
a_x2_x1_1 = -.1;
a_x2_x1_2 = .2;
beta = .1;
e_c_m = .1;
c_z_1 = .07;
c_z_2 = -.3;
gamma = .7;
var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
model;
[name='eq:x1', data_type='nonstationary']
diff(diff(x1)) = a_x1_0*(diff(x1(-1))-diff(x1bar(-1))) + a_x1_1*diff(diff(x1(-1))) + a_x1_2*diff(diff(x1(-2))) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;
[name='eq:x2', data_type='nonstationary']
diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(diff(x1(-1))) + a_x2_2*diff(diff(x1(-2))) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;
[name='eq:x1bar', data_type='nonstationary']
diff(x1bar) = diff(x1bar(-1)) + ex1bar;
[name='eq:x2bar', data_type='nonstationary']
x2bar = x2bar(-1) + ex2bar;
[name='eq:pac']
diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;
end;
shocks;
var ex1 = 1.0;
var ex2 = 1.0;
var ex1bar = 1.0;
var ex2bar = 1.0;
var ez = 1.0;
end;
// Build the companion matrix of the VAR model (toto).
get_companion_matrix('toto', 'pacman');
// Update the parameters of the PAC expectation model (h0 and h1 vectors).
pac.update.equation('pacman');
// Set initial conditions to zero. Please use more sensible values if any...
initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
// Simulate the model for 500 periods
TrueData = simul_backward_model(initialconditions, 500);