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Theoretical autocovariances: 

* at order 2 with non-stationary variables, fixed 2nd order mean correction
* when HP filtering (whether at order 1 or 2), consider all variables as stationary (closes #52)


git-svn-id: https://www.dynare.org/svn/dynare/trunk@3288 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
sebastien 2009-12-23 11:34:44 +00:00
parent 0ad1c611ee
commit e6a1916577
1 changed files with 12 additions and 7 deletions
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19
matlab/th_autocovariances.m
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@ -94,6 +94,9 @@ b = ghu1*M_.Sigma_e*ghu1';
ipred = nstatic+(1:npred)';
% state space representation for state variables only
[A,B] = kalman_transition_matrix(dr,ipred,1:nx,dr.transition_auxiliary_variables,M_.exo_nbr);
% Compute stationary variables (before HP filtering),
% and compute 2nd order mean correction on stationary variables (in case of
% HP filtering, this mean correction is computed *before* filtering)
if options_.order == 2 | options_.hp_filter == 0
[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.qz_criterium,options_.lyapunov_complex_threshold);
iky = inv_order_var(ivar);
@ -108,8 +111,9 @@ if options_.order == 2 | options_.hp_filter == 0
if options_.order == 2 % mean correction for 2nd order
Ex = (dr.ghs2(ikx)+dr.ghxx(ikx,:)*vx(:)+dr.ghuu(ikx,:)*M_.Sigma_e(:))/2;
Ex = (eye(n0)-AS(ikx,:))\Ex;
Gamma_y{nar+3} = AS(iky,:)*Ex+(dr.ghs2(iky)+dr.ghxx(iky,:)*vx(:)+...
dr.ghuu(iky,:)*M_.Sigma_e(:))/2;
Gamma_y{nar+3} = NaN*ones(nvar, 1);
Gamma_y{nar+3}(stationary_vars) = AS(iky,:)*Ex+(dr.ghs2(iky)+dr.ghxx(iky,:)*vx(:)+...
dr.ghuu(iky,:)*M_.Sigma_e(:))/2;
end
end
if options_.hp_filter == 0
@ -149,11 +153,12 @@ if options_.hp_filter == 0
end
end
else% ==> Theoretical HP filter.
if options_.order < 2
iky = inv_order_var(ivar);
aa = ghx(iky,:);
bb = ghu(iky,:);
end
% By construction, all variables are stationary when HP filtered
iky = inv_order_var(ivar);
stationary_vars = (1:length(ivar))';
aa = ghx(iky,:);
bb = ghu(iky,:);
lambda = options_.hp_filter;
ngrid = options_.hp_ngrid;
freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid));