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// --+ options: json=compute, stochastic +--
var y x z x1 z1 ;
varexo ey ex ez;
parameters alpha beta;
alpha = 1.0/3.0;
beta = 0.77;
model;
[name='eq4x1']
x1 = .5*x1(-1) + ex;
[name='eq4z1']
z1 = .8*z1(-1) + ez;
[name='eq4x']
x = x1^2/(1+x1^2);
[name='eq4z']
z = z1^2/(1+z1^2);
[name='eq4y']
y = alpha*x + (1-alpha)*z + beta*((1-alpha)*y(-1)+alpha*y(-2))+ey;
end;
/*
** Artificial dataset
*/
shocks;
var ex = .1;
var ez = .1;
var ey = .1;
end;
histval;
x1(0) = 0;
z1(0) = 0;
x(0) = 0;
z(0) = 0;
y(0) = 0;
y(-1) = 0;
end;
simulations = simul_backward_model([], 102);
/*
** Estimation by NLS
*/
eparams.alpha = .7;
eparams.beta = 1;
simulations.ey = dseries(NaN); // Reset residuals of the equation to NaN.
if ~isoctave
% Under Octave, estimate.nls (provided by matlab/+estimate/nls.m) is not
% accessible because there is a function which has the same name as the
% +estimate package, namely matlab/cli/estimate.m. This is a known Octave
% bug (https://savannah.gnu.org/bugs/?func=detailitem&item_id=46889).
estimate.nls('eq4y', eparams, simulations, dates('3Y'):simulations.dates(end));
end
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