76 lines
2.5 KiB
Modula-2
76 lines
2.5 KiB
Modula-2
// --+ options: stochastic,json=compute +--
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var foo z x y;
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varexo e_x e_y e_z;
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parameters a b c d e f beta ;
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a = .9;
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b = -.2;
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c = .3;
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f = .8;
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d = .5;
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e = .4;
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beta = 1/(1+.02);
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// Define a VAR model from a subset of equations in the model block.
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var_model(model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
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/* Define a VAR_EXPECTATION_MODEL
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** ------------------------------
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**
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** model_name: the name of the VAR_EXPECTATION_MODEL (mandatory).
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** var_model_name: the name of the VAR model used for the expectations (mandatory).
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** variable: the name of the variable to be forecasted (mandatory).
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** horizon: the horizon forecast (mandatory).
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** discount: the discount factor, which can be a value or a declared parameter (default is 1.0, no discounting).
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**
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**
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** The `horizon` parameter can be an integer in which case the (discounted) `horizon` step ahead forecast
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** is computed using the VAR model `var_model_name`. Alternatively, `horizon` can be a range. In this case
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** VAR_EXPECTATION_MODEL returns a discounted sum of expected values. If `horizon` is set equal to the range
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** 0:Inf, then VAR_EXPECTATION_MODEL computes:
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**
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** ∑ βʰ Eₜ[yₜ₊ₕ]
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**
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** where the sum is over h=0,…,∞ and the conditional expectations are computed with VAR model `var_model_name`.
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*/
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var_expectation_model(model_name = varexp, expression = x, auxiliary_model_name = toto, horizon = 2, discount = beta) ;
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model;
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[ name = 'X' ]
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x = a*x(-1) + b*x(-2) + c*z(-2) + e_x;
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[ name = 'Z' ]
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z = f*z(-1) + e_z;
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[ name = 'Y' ]
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y = d*y(-2) + e*z(-1) + e_y;
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foo = .5*foo(-1) + var_expectation(varexp);
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end;
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// Initialize the VAR expectation model, will build the companion matrix of the VAR.
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var_expectation.initialize('varexp')
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// Update VAR_EXPECTATION reduced form parameters
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var_expectation.update('varexp');
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// Print equations where the variable appears in
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search('x')
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search('y', 'withparamvalues')
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/*
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** REMARK The VAR model is such that x depends on past values of x
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** (xₜ₋₁ and xₜ₋₂) and on zₜ₋₂ ⇒ yₜ₋₁, yₜ₋₂ and zₜ₋₁ do not bring any
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** useful information for predicting xₜ₊₁. Consequently the reduced
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** form parameters associated to yₜ₋₁, yₜ₋₂ and zₜ₋₁ have to be zero.
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*/
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weights = M_.params(M_.var_expectation.varexp.param_indices);
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if weights(3) || ~weights(4) || weights(6) || ~weights(2) || ~weights(5) || ~weights(7) || weights(1)
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error('Wrong reduced form parameter for VAR_EXPECTATION_MODEL')
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end
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