Merge branch 'johannes_bandpass'
Stéphane Adjemian (Charybdis)
commit
6ea5bdde34
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@ -3703,13 +3703,27 @@ Number of points (burnin) dropped at the beginning of simulation before computin
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@item hp_filter = @var{DOUBLE}
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Uses HP filter with @math{\lambda} = @var{DOUBLE} before computing
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moments. Default: no filter.
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moments. If theoretical moments are requested, the spectrum of the model solution is filtered
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following the approach outlined in @cite{Uhlig (2001)}.
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Default: no filter.
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@item hp_ngrid = @var{INTEGER}
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Number of points in the grid for the discrete Inverse Fast Fourier
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Transform used in the HP filter computation. It may be necessary to
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increase it for highly autocorrelated processes. Default: @code{512}.
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@item bandpass_filter
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Uses a bandpass filter with the default passband before computing moments. If theoretical moments are
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requested, the spectrum of the model solution is filtered using an ideal bandpass
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filter. If empirical moments are requested, the @cite{Baxter and King (1999)}-filter
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is used.
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Default: no filter.
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@item bandpass_filter = @var{[HIGHEST_PERIODICITY LOWEST_PERIODICITY]}
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Uses a bandpass filter before computing moments. The passband is set to a periodicity of @code{HIGHEST_PERIODICITY}
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to @code{LOWEST_PERIODICITY}, e.g. 6 to 32 quarters if the model frequency is quarterly.
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Default: @code{[6,32]}.
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@item irf = @var{INTEGER}
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@anchor{irf}
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Number of periods on which to compute the IRFs. Setting @code{irf=0},
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@ -10774,7 +10788,7 @@ ts1 is a dseries object:
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@deftypefn {dseries} {@var{B} = } baxter_king_filter (@var{A}, @var{hf}, @var{lf}, @var{K})
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Implementation of the Baxter and King (1999) band pass filter for @dseries objects. This filter isolates business cycle fluctuations with a period of length ranging between @var{hf} (high frequency) to @var{lf} (low frequency) using a symmetric moving average smoother with @math{2K+1} points, so that K observations at the beginning and at the end of the sample are lost in the computation of the filter. The default value for @var{hf} is @math{6}, for @var{lf} is @math{32}, and for @var{K} is 12.
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Implementation of the @cite{Baxter and King (1999)} band pass filter for @dseries objects. This filter isolates business cycle fluctuations with a period of length ranging between @var{hf} (high frequency) to @var{lf} (low frequency) using a symmetric moving average smoother with @math{2K+1} points, so that K observations at the beginning and at the end of the sample are lost in the computation of the filter. The default value for @var{hf} is @math{6}, for @var{lf} is @math{32}, and for @var{K} is 12.
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@examplehead
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@example
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@ -12938,6 +12952,11 @@ Backus, David K., Patrick J. Kehoe, and Finn E. Kydland (1992):
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``International Real Business Cycles,'' @i{Journal of Political
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Economy}, 100(4), 745--775
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@item
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Baxter, Marianne and Robert G. King (1999):
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``Measuring Business Cycles: Approximate Band-pass Filters for Economic Time Series,''
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@i{Review of Economics and Statistics}, 81(4), 575--593
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@item
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Boucekkine, Raouf (1995): ``An alternative methodology for solving
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nonlinear forward-looking models,'' @i{Journal of Economic Dynamics
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@ -13138,6 +13157,11 @@ Smets, Frank and Rafael Wouters (2003): ``An Estimated Dynamic
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Stochastic General Equilibrium Model of the Euro Area,'' @i{Journal of
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the European Economic Association}, 1(5), 1123--1175
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@item
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Uhlig, Harald (2001): ``A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily,''
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in @i{Computational Methods for the Study of Dynamic
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Economies}, Eds. Ramon Marimon and Andrew Scott, Oxford University Press, 30--61
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@item
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Villemot, Sébastien (2011): ``Solving rational expectations models at
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first order: what Dynare does,'' @i{Dynare Working Papers}, 2,
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@ -1,4 +1,4 @@
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Format: http://www.debian.org/doc/packaging-manuals/copyright-format/1.0/
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Format: http://www.debian.org/doc/packaging-manuals/copyright-format/1.0/
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Upstream-Name: Dynare
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Upstream-Contact: Dynare Team, whose members in 2015 are:
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Stéphane Adjemian <stephane.adjemian@univ-lemans.fr>
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@ -76,6 +76,11 @@ Copyright: 2008-2012 VZLU Prague, a.s.
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2014 Dynare Team
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License: GPL-3+
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Files: matlab/one_sided_hp_filter.m
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Copyright: 2010-2015 Alexander Meyer-Gohde
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2015 Dynare Team
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License: GPL-3+
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Files: matlab/optimization/simpsa.m matlab/optimization/simpsaget.m matlab/optimization/simpsaset.m
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Copyright: 2005 Henning Schmidt, FCC, henning@fcc.chalmers.se
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2006 Brecht Donckels, BIOMATH, brecht.donckels@ugent.be
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@ -1,11 +1,25 @@
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function [omega,f] = UnivariateSpectralDensity(dr,var_list)
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function [oo_] = UnivariateSpectralDensity(M_,oo_,options_,var_list)
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% This function computes the theoretical spectral density of each
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% endogenous variable declared in var_list. Results are stored in
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% oo_ and may be plotted. Plots are saved into the graphs-folder.
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% oo_.SpectralDensity and may be plotted. Plots are saved into the
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% graphs-folder.
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%
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% INPUTS
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% M_ [structure] Dynare's model structure
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% oo_ [structure] Dynare's results structure
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% options_ [structure] Dynare's options structure
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% var_list [integer] Vector of indices for a subset of variables.
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%
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% OUTPUTS
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% oo_ [structure] Dynare's results structure,
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% containing the subfield
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% SpectralDensity with fields freqs
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% and density, which are of size nvar*ngrid.
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%
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% Adapted from th_autocovariances.m.
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% Copyright (C) 2006-2013 Dynare Team
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% Copyright (C) 2006-2015 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -22,10 +36,6 @@ function [omega,f] = UnivariateSpectralDensity(dr,var_list)
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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global options_ oo_ M_
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omega = []; f = [];
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if options_.order > 1
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disp('UnivariateSpectralDensity :: I Cannot compute the theoretical spectral density')
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@ -33,12 +43,7 @@ if options_.order > 1
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disp('Please set order = 1. I abort')
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return
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end
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pltinfo = options_.SpectralDensity.plot;
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cutoff = options_.SpectralDensity.cutoff;
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sdl = options_.SpectralDensity.sdl;
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omega = (0:sdl:pi)';
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GridSize = length(omega);
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exo_names_orig_ord = M_.exo_names_orig_ord;
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if isoctave
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warning('off', 'Octave:divide-by-zero')
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else
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@ -60,22 +65,19 @@ for i=1:nvar
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ivar(i) = i_tmp;
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end
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end
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f = zeros(nvar,GridSize);
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ghx = dr.ghx;
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ghu = dr.ghu;
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ghx = oo_.dr.ghx;
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ghu = oo_.dr.ghu;
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nspred = M_.nspred;
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nstatic = M_.nstatic;
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kstate = dr.kstate;
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order = dr.order_var;
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kstate = oo_.dr.kstate;
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order = oo_.dr.order_var;
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iv(order) = [1:length(order)];
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nx = size(ghx,2);
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ikx = [nstatic+1:nstatic+nspred];
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A = zeros(nx,nx);
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k0 = kstate(find(kstate(:,2) <= M_.maximum_lag+1),:);
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i0 = find(k0(:,2) == M_.maximum_lag+1);
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i00 = i0;
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n0 = length(i0);
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A(i0,:) = ghx(ikx,:);
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AS = ghx(:,i0);
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ghu1 = zeros(nx,M_.exo_nbr);
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ghu1(i0,:) = ghu(ikx,:);
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@ -91,92 +93,74 @@ for i=M_.maximum_lag:-1:2
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AS(:,j1) = AS(:,j1)+ghx(:,i1);
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i0 = i1;
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end
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Gamma = zeros(nvar,cutoff+1);
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[A,B] = kalman_transition_matrix(dr,ikx',1:nx,M_.exo_nbr);
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[A,B] = kalman_transition_matrix(oo_.dr,ikx',1:nx,M_.exo_nbr);
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[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],[],options_.debug);
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iky = iv(ivar);
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if ~isempty(u)
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iky = iky(find(any(abs(ghx(iky,:)*u) < options_.Schur_vec_tol,2)));
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ivar = dr.order_var(iky);
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ivar = oo_.dr.order_var(iky);
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end
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iky = iv(ivar);
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aa = ghx(iky,:);
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bb = ghu(iky,:);
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if options_.hp_filter == 0
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tmp = aa*vx*aa'+ bb*M_.Sigma_e*bb';
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k = find(abs(tmp) < 1e-12);
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tmp(k) = 0;
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Gamma(:,1) = diag(tmp);
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vxy = (A*vx*aa'+ghu1*M_.Sigma_e*bb');
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tmp = aa*vxy;
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k = find(abs(tmp) < 1e-12);
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tmp(k) = 0;
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Gamma(:,2) = diag(tmp);
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for i=2:cutoff
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vxy = A*vxy;
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tmp = aa*vxy;
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k = find(abs(tmp) < 1e-12);
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tmp(k) = 0;
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Gamma(:,i+1) = diag(tmp);
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end
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else
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iky = iv(ivar);
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aa = ghx(iky,:);
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bb = ghu(iky,:);
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ngrid = options_.hp_ngrid; %number of grid points
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freqs = (0 : pi/(ngrid-1):pi)'; % grid on which to compute
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tpos = exp( sqrt(-1)*freqs); %positive frequencies
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tneg = exp(-sqrt(-1)*freqs); %negative frequencies
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if options_.one_sided_hp_filter
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error('UnivariateSpectralDensity:: spectral density estimate not available with one-sided HP filter')
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elseif options_.hp_filter == 0 && ~options_.bandpass.indicator %do not filter
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filter_gain=ones(ngrid,1);
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elseif ~(options_.hp_filter == 0 && ~options_.bandpass.indicator) && options_.bandpass.indicator %filter with bandpass
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filter_gain = zeros(1,ngrid);
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lowest_periodicity=options_.bandpass.passband(2);
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highest_periodicity=options_.bandpass.passband(1);
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highest_periodicity=max(2,highest_periodicity); % restrict to upper bound of pi
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filter_gain(freqs>=2*pi/lowest_periodicity & freqs<=2*pi/highest_periodicity)=1;
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filter_gain(freqs<=-2*pi/lowest_periodicity+2*pi & freqs>=-2*pi/highest_periodicity+2*pi)=1;
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elseif ~(options_.hp_filter == 0 && ~options_.bandpass.indicator) && ~options_.bandpass.indicator %filter with HP-filter
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lambda = options_.hp_filter;
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ngrid = options_.hp_ngrid;
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freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid));
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tpos = exp( sqrt(-1)*freqs);
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tneg = exp(-sqrt(-1)*freqs);
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hp1 = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
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mathp_col = [];
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IA = eye(size(A,1));
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IE = eye(M_.exo_nbr);
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for ig = 1:ngrid
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f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*ghu1;IE]...
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*M_.Sigma_e*[ghu1'*inv(IA-A'*tpos(ig)) IE]); % state variables
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g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
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f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
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mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
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% for ifft
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end;
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imathp_col = real(ifft(mathp_col))*(2*pi);
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tmp = reshape(imathp_col(1,:),nvar,nvar);
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k = find(abs(tmp)<1e-12);
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tmp(k) = 0;
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Gamma(:,1) = diag(tmp);
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sy = sqrt(Gamma(:,1));
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sy = sy *sy';
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for i=1:cutoff-1
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tmp = reshape(imathp_col(i+1,:),nvar,nvar)./sy;
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k = find(abs(tmp) < 1e-12);
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tmp(k) = 0;
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Gamma(:,i+1) = diag(tmp);
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end
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filter_gain = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
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end
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H = 1:cutoff;
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mathp_col = NaN(ngrid,length(ivar)^2);
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IA = eye(size(A,1));
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IE = eye(M_.exo_nbr);
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for ig = 1:ngrid
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f_omega =(1/(2*pi))*( [(IA-A*tneg(ig))\ghu1;IE]...
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*M_.Sigma_e*[ghu1'/(IA-A'*tpos(ig)) IE]); % state variables
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g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
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f_hp = filter_gain(ig)^2*g_omega; % spectral density of selected filtered series
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mathp_col(ig,:) = (f_hp(:))'; % store as matrix row
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end;
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f = zeros(nvar,ngrid);
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for i=1:nvar
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f(i,:) = Gamma(i,1)/(2*pi) + Gamma(i,H+1)*cos(H'*omega')/pi;
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f(i,:) = real(mathp_col(:,(i-1)*nvar+i)); %read out spectral density
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end
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oo_.SpectralDensity.freqs=freqs;
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oo_.SpectralDensity.density=f;
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if isoctave
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warning('on', 'Octave:divide-by-zero')
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else
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warning on MATLAB:dividebyzero
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end
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if pltinfo
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if options_.nograph == 0
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if ~exist(M_.fname, 'dir')
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mkdir('.',M_.fname);
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end
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if ~exist([M_.fname '/graphs'])
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if ~exist([M_.fname '/graphs'],'dir')
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mkdir(M_.fname,'graphs');
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end
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for i= 1:nvar
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hh = dyn_figure(options_,'Name',['Spectral Density of ' deblank(M_.endo_names(ivar(i),:)) '.']);
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plot(omega,f(i,:),'-k','linewidth',2)
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plot(freqs,f(i,:),'-k','linewidth',2)
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xlabel('0 \leq \omega \leq \pi')
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ylabel('f(\omega)')
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box on
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@ -0,0 +1,15 @@
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function title=add_filter_subtitle(title,options_)
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if ~options_.hp_filter && ~options_.one_sided_hp_filter && ~options_.bandpass.indicator %do not filter
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%nothing to add here
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elseif ~options_.hp_filter && ~options_.one_sided_hp_filter && options_.bandpass.indicator
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title = [title ' (Bandpass filter, (' ...
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num2str(options_.bandpass.passband(1)),' ',num2str(options_.bandpass.passband(2)), '))'];
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elseif options_.hp_filter && ~options_.one_sided_hp_filter && ~options_.bandpass.indicator %filter with HP-filter
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title = [title ' (HP filter, lambda = ' ...
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num2str(options_.hp_filter) ')'];
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elseif ~options_.hp_filter && options_.one_sided_hp_filter && ~options_.bandpass.indicator
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title = [title ' (One-sided HP filter, lambda = ' ...
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num2str(options_.one_sided_hp_filter) ')'];
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end
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end
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@ -106,7 +106,7 @@ if ismember('moments', varargin) % Prior simulations (2nd order moments).
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% Solve model
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[dr,info, M_ ,options_ , oo_] = resol(0, M_ , options_ ,oo_);
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% Compute and display second order moments
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disp_th_moments(oo_.dr,[]);
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oo_=disp_th_moments(oo_.dr,[],M_,options_,oo_);
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skipline(2)
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donesomething = true;
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end
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@ -1,7 +1,17 @@
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function disp_moments(y,var_list)
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function oo_=disp_moments(y,var_list,M_,options_,oo_)
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% function disp_moments(y,var_list,M_,options_,oo_)
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% Displays moments of simulated variables
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% INPUTS
|
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% y [double] nvar*nperiods vector of simulated variables.
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% var_list [char] nvar character array with names of variables.
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% M_ [structure] Dynare's model structure
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% oo_ [structure] Dynare's results structure
|
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% options_ [structure] Dynare's options structure
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%
|
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% OUTPUTS
|
||||
% oo_ [structure] Dynare's results structure,
|
||||
|
||||
% Copyright (C) 2001-2012 Dynare Team
|
||||
% Copyright (C) 2001-2015 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
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@ -18,8 +28,6 @@ function disp_moments(y,var_list)
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|||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
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|
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global M_ options_ oo_
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warning_old_state = warning;
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warning off
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@ -42,11 +50,8 @@ y = y(ivar,options_.drop+1:end)';
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|||
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m = mean(y);
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||||
if options_.hp_filter
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[hptrend,y] = sample_hp_filter(y,options_.hp_filter);
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else
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y = bsxfun(@minus, y, m);
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end
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% filter series
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y=get_filtered_time_series(y,m,options_);
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||||
s2 = mean(y.*y);
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s = sqrt(s2);
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@ -54,17 +59,20 @@ oo_.mean = transpose(m);
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oo_.var = y'*y/size(y,1);
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||||
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||||
labels = deblank(M_.endo_names(ivar,:));
|
||||
labels_TeX = deblank(M_.endo_names_tex(ivar,:));
|
||||
|
||||
if options_.nomoments == 0
|
||||
z = [ m' s' s2' (mean(y.^3)./s2.^1.5)' (mean(y.^4)./(s2.*s2)-3)' ];
|
||||
title='MOMENTS OF SIMULATED VARIABLES';
|
||||
if options_.hp_filter
|
||||
title = [title ' (HP filter, lambda = ' ...
|
||||
num2str(options_.hp_filter) ')'];
|
||||
end
|
||||
|
||||
title=add_filter_subtitle(title,options_);
|
||||
|
||||
headers=char('VARIABLE','MEAN','STD. DEV.','VARIANCE','SKEWNESS', ...
|
||||
'KURTOSIS');
|
||||
dyntable(title,headers,labels,z,size(labels,2)+2,16,6);
|
||||
if options_.TeX
|
||||
dyn_latex_table(M_,title,'sim_moments',headers,labels_TeX,z,size(labels,2)+2,16,6);
|
||||
end
|
||||
end
|
||||
|
||||
if options_.nocorr == 0
|
||||
|
|
@ -74,12 +82,16 @@ if options_.nocorr == 0
|
|||
end
|
||||
if options_.noprint == 0
|
||||
title = 'CORRELATION OF SIMULATED VARIABLES';
|
||||
if options_.hp_filter
|
||||
title = [title ' (HP filter, lambda = ' ...
|
||||
num2str(options_.hp_filter) ')'];
|
||||
end
|
||||
|
||||
title=add_filter_subtitle(title,options_);
|
||||
|
||||
headers = char('VARIABLE',M_.endo_names(ivar,:));
|
||||
dyntable(title,headers,labels,corr,size(labels,2)+2,8,4);
|
||||
if options_.TeX
|
||||
headers = char('VARIABLE',M_.endo_names_tex(ivar,:));
|
||||
lh = size(labels,2)+2;
|
||||
dyn_latex_table(M_,title,'sim_corr_matrix',headers,labels_TeX,corr,size(labels,2)+2,8,4);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
|
@ -96,13 +108,91 @@ if ar > 0
|
|||
end
|
||||
if options_.noprint == 0
|
||||
title = 'AUTOCORRELATION OF SIMULATED VARIABLES';
|
||||
if options_.hp_filter
|
||||
title = [title ' (HP filter, lambda = ' ...
|
||||
num2str(options_.hp_filter) ')'];
|
||||
end
|
||||
title=add_filter_subtitle(title,options_);
|
||||
headers = char('VARIABLE',int2str([1:ar]'));
|
||||
dyntable(title,headers,labels,autocorr,size(labels,2)+2,8,4);
|
||||
if options_.TeX
|
||||
headers = char('VARIABLE',int2str([1:ar]'));
|
||||
lh = size(labels,2)+2;
|
||||
dyn_latex_table(M_,title,'sim_autocorr_matrix',headers,labels_TeX,autocorr,size(labels_TeX,2)+2,8,4);
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
|
||||
if ~options_.nodecomposition
|
||||
if M_.exo_nbr == 1
|
||||
oo_.variance_decomposition = 100*ones(nvar,1);
|
||||
else
|
||||
oo_.variance_decomposition=zeros(nvar,M_.exo_nbr);
|
||||
%get starting values
|
||||
if isempty(M_.endo_histval)
|
||||
y0 = oo_.dr.ys;
|
||||
else
|
||||
y0 = M_.endo_histval;
|
||||
end
|
||||
%back out shock matrix used for generating y
|
||||
i_exo_var = setdiff([1:M_.exo_nbr],find(diag(M_.Sigma_e) == 0)); % find shocks with 0 variance
|
||||
chol_S = chol(M_.Sigma_e(i_exo_var,i_exo_var)); %decompose rest
|
||||
shock_mat=zeros(options_.periods,M_.exo_nbr); %initialize
|
||||
shock_mat(:,i_exo_var)=oo_.exo_simul(:,i_exo_var)/chol_S; %invert construction of oo_.exo_simul from simult.m
|
||||
|
||||
for shock_iter=1:length(i_exo_var)
|
||||
temp_shock_mat=zeros(size(shock_mat));
|
||||
temp_shock_mat(:,i_exo_var(shock_iter))=shock_mat(:,i_exo_var(shock_iter));
|
||||
temp_shock_mat(:,i_exo_var) = temp_shock_mat(:,i_exo_var)*chol_S;
|
||||
y_sim_one_shock = simult_(y0,oo_.dr,temp_shock_mat,options_.order);
|
||||
y_sim_one_shock=y_sim_one_shock(ivar,1+options_.drop+1:end)';
|
||||
y_sim_one_shock=get_filtered_time_series(y_sim_one_shock,mean(y_sim_one_shock),options_);
|
||||
oo_.variance_decomposition(:,i_exo_var(shock_iter))=var(y_sim_one_shock)./s2*100;
|
||||
end
|
||||
if ~options_.noprint %options_.nomoments == 0
|
||||
skipline()
|
||||
title='VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent)';
|
||||
|
||||
title=add_filter_subtitle(title,options_);
|
||||
|
||||
headers = M_.exo_names;
|
||||
headers(M_.exo_names_orig_ord,:) = headers;
|
||||
headers = char(' ',headers);
|
||||
lh = size(deblank(M_.endo_names(ivar,:)),2)+2;
|
||||
dyntable(title,char(headers,'Tot. lin. contr.'),deblank(M_.endo_names(ivar,:)),[oo_.variance_decomposition sum(oo_.variance_decomposition,2)],lh,8,2);
|
||||
if options_.TeX
|
||||
headers=M_.exo_names_tex;
|
||||
headers = char(' ',headers);
|
||||
labels = deblank(M_.endo_names_tex(ivar,:));
|
||||
lh = size(labels,2)+2;
|
||||
dyn_latex_table(M_,title,'sim_var_decomp',char(headers,'Tot. lin. contr.'),labels_TeX,[oo_.variance_decomposition sum(oo_.variance_decomposition,2)],lh,8,2);
|
||||
end
|
||||
|
||||
if options_.order == 1
|
||||
fprintf('Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples\n\n')
|
||||
else
|
||||
fprintf('Note: numbers do not add up to 100 due to i) non-zero correlation of simulated shocks in small samples and ii) nonlinearity\n\n')
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
end
|
||||
|
||||
warning(warning_old_state);
|
||||
end
|
||||
|
||||
function y=get_filtered_time_series(y,m,options_)
|
||||
|
||||
if options_.hp_filter && ~options_.one_sided_hp_filter && ~options_.bandpass.indicator
|
||||
[hptrend,y] = sample_hp_filter(y,options_.hp_filter);
|
||||
elseif ~options_.hp_filter && options_.one_sided_hp_filter && ~options_.bandpass.indicator
|
||||
[hptrend,y] = one_sided_hp_filter(y,options_.one_sided_hp_filter);
|
||||
elseif ~options_.hp_filter && ~options_.one_sided_hp_filter && options_.bandpass.indicator
|
||||
data_temp=dseries(y,'0q1');
|
||||
data_temp=baxter_king_filter(data_temp,options_.bandpass.passband(1),options_.bandpass.passband(2),200);
|
||||
y=data_temp.data;
|
||||
elseif ~options_.hp_filter && ~options_.one_sided_hp_filter && ~options_.bandpass.indicator
|
||||
y = bsxfun(@minus, y, m);
|
||||
else
|
||||
error('disp_moments:: You cannot use more than one filter at the same time')
|
||||
end
|
||||
|
||||
end
|
||||
|
|
@ -1,7 +1,7 @@
|
|||
function disp_th_moments(dr,var_list)
|
||||
function oo_=disp_th_moments(dr,var_list,M_,options_,oo_)
|
||||
% Display theoretical moments of variables
|
||||
|
||||
% Copyright (C) 2001-2013 Dynare Team
|
||||
% Copyright (C) 2001-2015 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
|
|
@ -18,10 +18,10 @@ function disp_th_moments(dr,var_list)
|
|||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
global M_ oo_ options_
|
||||
|
||||
nodecomposition = options_.nodecomposition;
|
||||
|
||||
if options_.one_sided_hp_filter
|
||||
error(['disp_th_moments:: theoretical moments incompatible with one-sided HP filter. Use simulated moments instead'])
|
||||
end
|
||||
if size(var_list,1) == 0
|
||||
var_list = M_.endo_names(1:M_.orig_endo_nbr, :);
|
||||
end
|
||||
|
|
@ -62,13 +62,16 @@ if size(stationary_vars, 1) > 0
|
|||
else
|
||||
title='THEORETICAL MOMENTS';
|
||||
end
|
||||
if options_.hp_filter
|
||||
title = [title ' (HP filter, lambda = ' num2str(options_.hp_filter) ')'];
|
||||
end
|
||||
title=add_filter_subtitle(title,options_);
|
||||
headers=char('VARIABLE','MEAN','STD. DEV.','VARIANCE');
|
||||
labels = deblank(M_.endo_names(ivar,:));
|
||||
lh = size(labels,2)+2;
|
||||
dyntable(title,headers,labels,z,lh,11,4);
|
||||
if options_.TeX
|
||||
labels = deblank(M_.endo_names_tex(ivar,:));
|
||||
lh = size(labels,2)+2;
|
||||
dyn_latex_table(M_,title,'th_moments',headers,labels,z,lh,11,4);
|
||||
end
|
||||
|
||||
if M_.exo_nbr > 1 && ~nodecomposition
|
||||
skipline()
|
||||
|
|
@ -77,10 +80,7 @@ if size(stationary_vars, 1) > 0
|
|||
else
|
||||
title='VARIANCE DECOMPOSITION (in percent)';
|
||||
end
|
||||
if options_.hp_filter
|
||||
title = [title ' (HP filter, lambda = ' ...
|
||||
num2str(options_.hp_filter) ')'];
|
||||
end
|
||||
title=add_filter_subtitle(title,options_);
|
||||
headers = M_.exo_names;
|
||||
headers(M_.exo_names_orig_ord,:) = headers;
|
||||
headers = char(' ',headers);
|
||||
|
|
@ -88,6 +88,13 @@ if size(stationary_vars, 1) > 0
|
|||
dyntable(title,headers,deblank(M_.endo_names(ivar(stationary_vars), ...
|
||||
:)),100* ...
|
||||
oo_.gamma_y{options_.ar+2}(stationary_vars,:),lh,8,2);
|
||||
if options_.TeX
|
||||
headers=M_.exo_names_tex;
|
||||
headers = char(' ',headers);
|
||||
labels = deblank(M_.endo_names_tex(ivar(stationary_vars),:));
|
||||
lh = size(labels,2)+2;
|
||||
dyn_latex_table(M_,title,'th_var_decomp_uncond',headers,labels,100*oo_.gamma_y{options_.ar+2}(stationary_vars,:),lh,8,2);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
|
@ -127,13 +134,17 @@ if options_.nocorr == 0 && size(stationary_vars, 1) > 0
|
|||
else
|
||||
title='MATRIX OF CORRELATIONS';
|
||||
end
|
||||
if options_.hp_filter
|
||||
title = [title ' (HP filter, lambda = ' num2str(options_.hp_filter) ')'];
|
||||
end
|
||||
title=add_filter_subtitle(title,options_);
|
||||
labels = deblank(M_.endo_names(ivar(i1),:));
|
||||
headers = char('Variables',labels);
|
||||
lh = size(labels,2)+2;
|
||||
dyntable(title,headers,labels,corr,lh,8,4);
|
||||
if options_.TeX
|
||||
labels = deblank(M_.endo_names_tex(ivar(i1),:));
|
||||
headers=char('Variables',labels);
|
||||
lh = size(labels,2)+2;
|
||||
dyn_latex_table(M_,title,'th_corr_matrix',headers,labels,corr,lh,8,4);
|
||||
end
|
||||
end
|
||||
end
|
||||
if options_.ar > 0 && size(stationary_vars, 1) > 0
|
||||
|
|
@ -149,12 +160,16 @@ if options_.ar > 0 && size(stationary_vars, 1) > 0
|
|||
else
|
||||
title='COEFFICIENTS OF AUTOCORRELATION';
|
||||
end
|
||||
if options_.hp_filter
|
||||
title = [title ' (HP filter, lambda = ' num2str(options_.hp_filter) ')'];
|
||||
end
|
||||
title=add_filter_subtitle(title,options_);
|
||||
labels = deblank(M_.endo_names(ivar(i1),:));
|
||||
headers = char('Order ',int2str([1:options_.ar]'));
|
||||
lh = size(labels,2)+2;
|
||||
dyntable(title,headers,labels,z,lh,8,4);
|
||||
if options_.TeX
|
||||
labels = deblank(M_.endo_names_tex(ivar(i1),:));
|
||||
headers=char('Order ',int2str([1:options_.ar]'));
|
||||
lh = size(labels,2)+2;
|
||||
dyn_latex_table(M_,title,'th_autocorr_matrix',headers,labels,z,lh,8,4);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
|
|
|||
|
|
@ -31,11 +31,13 @@ function display_conditional_variance_decomposition(conditional_decomposition_ar
|
|||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
if options_.order == 2
|
||||
skipline()
|
||||
disp('APPROXIMATED CONDITIONAL VARIANCE DECOMPOSITION (in percent)')
|
||||
skipline()
|
||||
title='APPROXIMATED CONDITIONAL VARIANCE DECOMPOSITION (in percent)';
|
||||
disp(title)
|
||||
else
|
||||
skipline()
|
||||
disp('CONDITIONAL VARIANCE DECOMPOSITION (in percent)')
|
||||
skipline()
|
||||
title='CONDITIONAL VARIANCE DECOMPOSITION (in percent)';
|
||||
disp(title)
|
||||
end
|
||||
|
||||
vardec_i = zeros(length(SubsetOfVariables),M_.exo_nbr);
|
||||
|
|
@ -54,4 +56,10 @@ for i=1:length(Steps)
|
|||
dyntable('',headers,...
|
||||
deblank(M_.endo_names(SubsetOfVariables,:)),...
|
||||
vardec_i,lh,8,2);
|
||||
if options_.TeX
|
||||
labels_TeX = deblank(M_.endo_names_tex(SubsetOfVariables,:));
|
||||
headers_TeX=char('',deblank(M_.exo_names_tex));
|
||||
lh = size(labels_TeX,2)+2;
|
||||
dyn_latex_table(M_,[title,'; Period ' int2str(Steps(i))],['th_var_decomp_cond_h',int2str(Steps(i))],headers_TeX,labels_TeX,vardec_i,lh,8,2);
|
||||
end
|
||||
end
|
||||
|
|
@ -0,0 +1,73 @@
|
|||
function dyn_latex_table(M_,title,LaTeXtitle,headers,labels,values,label_width,val_width,val_precis)
|
||||
|
||||
OutputDirectoryName = CheckPath('Output',M_.dname);
|
||||
|
||||
%% get width of label column
|
||||
if ~isempty(label_width)
|
||||
label_width = max(size(deblank(char(headers(1,:),labels)),2)+2, ...
|
||||
label_width);
|
||||
else %use default length
|
||||
label_width = max(size(deblank(char(headers(1,:),labels)),2))+2;
|
||||
end
|
||||
label_format_leftbound = sprintf('$%%-%ds$',label_width);
|
||||
|
||||
%% get width of label column
|
||||
if all(~isfinite(values))
|
||||
values_length = 4;
|
||||
else
|
||||
values_length = max(ceil(max(max(log10(abs(values(isfinite(values))))))),1)+val_precis+1;
|
||||
end
|
||||
if any(values) < 0 %add one character for minus sign
|
||||
values_length = values_length+1;
|
||||
end
|
||||
|
||||
%% get width of header strings
|
||||
headers_length = max(size(deblank(headers(2:end,:)),2));
|
||||
if ~isempty(val_width)
|
||||
val_width = max(max(headers_length,values_length)+4,val_width);
|
||||
else
|
||||
val_width = max(headers_length,values_length)+4;
|
||||
end
|
||||
value_format = sprintf('%%%d.%df',val_width,val_precis);
|
||||
header_string_format = sprintf('$%%%ds$',val_width);
|
||||
|
||||
%Create and print header string
|
||||
if length(headers) > 0
|
||||
header_string = sprintf(label_format_leftbound ,deblank(headers(1,:)));
|
||||
header_code_string='l|';
|
||||
for i=2:size(headers,1)
|
||||
header_string = [header_string '\t & \t ' sprintf(header_string_format,strrep(deblank(headers(i,:)),'\','\\'))];
|
||||
header_code_string= [header_code_string 'c'];
|
||||
end
|
||||
end
|
||||
header_string=[header_string '\\\\\n'];
|
||||
|
||||
filename = [OutputDirectoryName '/' M_.fname '_' LaTeXtitle '.TeX'];
|
||||
fidTeX = fopen(filename,'w');
|
||||
fprintf(fidTeX,['%% ' datestr(now,0)]);
|
||||
fprintf(fidTeX,' \n');
|
||||
fprintf(fidTeX,' \n');
|
||||
fprintf(fidTeX,'\\begin{center}\n');
|
||||
fprintf(fidTeX,['\\begin{longtable}{%s} \n'],header_code_string);
|
||||
|
||||
fprintf(fidTeX,['\\caption{',title,'}\\\\\n ']);
|
||||
fprintf(fidTeX,['\\label{Table:',LaTeXtitle,'}\\\\\n']);
|
||||
fprintf(fidTeX,'\\hline\\hline \\\\ \n');
|
||||
fprintf(fidTeX,header_string);
|
||||
fprintf(fidTeX,'\\hline \\endfirsthead \n');
|
||||
fprintf(fidTeX,'\\caption{(continued)}\\\\\n ');
|
||||
fprintf(fidTeX,'\\hline\\hline \\\\ \n');
|
||||
fprintf(fidTeX,header_string);
|
||||
fprintf(fidTeX,'\\hline \\endhead \n');
|
||||
fprintf(fidTeX,['\\hline \\multicolumn{',num2str(size(headers,1)),'}{r}{(Continued on next page)} \\\\ \\hline \\endfoot \n']);
|
||||
fprintf(fidTeX,'\\hline \\hline \\endlastfoot \n');
|
||||
for i=1:size(values,1)
|
||||
fprintf(fidTeX,label_format_leftbound,deblank(labels(i,:)));
|
||||
fprintf(fidTeX,['\t & \t' value_format],values(i,:));
|
||||
fprintf(fidTeX,' \\\\ \n');
|
||||
end
|
||||
|
||||
fprintf(fidTeX,'\\end{longtable}\n ');
|
||||
fprintf(fidTeX,'\\end{center}\n');
|
||||
fprintf(fidTeX,'%% End of TeX file.\n');
|
||||
fclose(fidTeX);
|
||||
|
|
@ -153,7 +153,7 @@ options_.impulse_responses.plot_threshold=1e-10;
|
|||
options_.relative_irf = 0;
|
||||
options_.ar = 5;
|
||||
options_.hp_filter = 0;
|
||||
options_.one_sided_hp_filter = 1600;
|
||||
options_.one_sided_hp_filter = 0;
|
||||
options_.hp_ngrid = 512;
|
||||
options_.nodecomposition = 0;
|
||||
options_.nomoments = 0;
|
||||
|
|
|
|||
|
|
@ -0,0 +1,113 @@
|
|||
function [ytrend,ycycle]=one_sided_hp_filter(y,lambda,x_user,P_user,discard)
|
||||
% function [ytrend,ycycle]=one_sided_hp_filter(y,lambda,x_user,P_user,discard)
|
||||
% Conducts one-sided HP-filtering, derived using the Kalman filter
|
||||
%
|
||||
% Inputs:
|
||||
% y [T*n] double data matrix in column format
|
||||
% lambda [scalar] Smoothing parameter. Default value of 1600 will be used.
|
||||
% x_user [2*n] double matrix with initial values of the state
|
||||
% estimate for each variable in y. The underlying
|
||||
% state vector is 2x1 for each variable in y.
|
||||
% Default: use backwards extrapolations
|
||||
% based on the first two observations
|
||||
% P_user [n*1] struct structural array with n elements, each a two
|
||||
% 2x2 matrix of intial MSE estimates for each
|
||||
% variable in y.
|
||||
% Default: matrix with large variances
|
||||
% discard [scalar] number of initial periods to be discarded
|
||||
% Default: 0
|
||||
%
|
||||
% Output:
|
||||
% ytrend [(T-discard)*n] matrix of extracted trends
|
||||
% ycycle [(T-discard)*n] matrix of extracted deviations from the extracted trends
|
||||
%
|
||||
% Algorithms:
|
||||
%
|
||||
% Implements the procedure described on p. 301 of Stock, J.H. and M.W. Watson (1999):
|
||||
% "Forecasting inflation," Journal of Monetary Economics, vol. 44(2), pages 293-335, October.
|
||||
% that states on page 301:
|
||||
%
|
||||
% "The one-sided HP trend estimate is constructed as the Kalman
|
||||
% filter estimate of tau_t in the model:
|
||||
%
|
||||
% y_t=tau_t+epsilon_t
|
||||
% (1-L)^2 tau_t=eta_t"
|
||||
%
|
||||
% The Kalman filter notation follows Chapter 13 of Hamilton, J.D. (1994).
|
||||
% Time Series Analysis, with the exception of H, which is equivalent to his H'.
|
||||
|
||||
|
||||
% Copyright (C) 200?-2015 Alexander Meyer-Gohde
|
||||
% Copyright (C) 2015 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
if nargin < 2 || isempty(lambda)
|
||||
lambda = 1600; %If the user didn't provide a value for lambda, set it to the default value 1600
|
||||
end
|
||||
[T,n] = size (y);% Calculate the number of periods and the number of variables in the series
|
||||
|
||||
%Set up state space
|
||||
q=1/lambda; % the signal-to-noise ration: i.e. var eta_t / var epsilon_t
|
||||
F=[2,-1;
|
||||
1,0]; % state transition matrix
|
||||
H=[1,0]; % observation matrix
|
||||
Q=[q,0;
|
||||
0,0]; % covariance matrix state equation errors
|
||||
R=1; % variance observation equation error
|
||||
|
||||
for k=1:n %Run the Kalman filter for each variable
|
||||
if nargin < 4 || isempty(x_user) %no intial value for state, extrapolate back two periods from the observations
|
||||
x=[2*y(1,k)-y(2,k);
|
||||
3*y(1,k)-2*y(2,k)];
|
||||
else
|
||||
x=x_user(:,k);
|
||||
end
|
||||
if nargin < 4 || isempty(P_user) %no initial value for the MSE, set a rather high one
|
||||
P= [1e5 0;
|
||||
0 1e5];
|
||||
else
|
||||
P=P_user{k};
|
||||
end
|
||||
|
||||
for j=1:T %Get the estimates for each period
|
||||
[x,P]=kalman_update(F,H,Q,R,y(j,k),x,P); %get new state estimate and update recursion
|
||||
ytrend(j,k)=x(2);%second state is trend estimate
|
||||
end
|
||||
end
|
||||
|
||||
if nargout==2
|
||||
ycycle=y-ytrend;
|
||||
end
|
||||
|
||||
if nargin==5 %user provided a discard parameter
|
||||
ytrend=ytrend(discard+1:end,:);%Remove the first "discard" periods from the trend series
|
||||
if nargout==2
|
||||
ycycle=ycycle(discard+1:end,:);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
function [x,P]=kalman_update(F,H,Q,R,obs,x,P)
|
||||
% Updates the Kalman filter estimation of the state and MSE
|
||||
S=H*P*H'+R;
|
||||
K=F*P*H';
|
||||
K=K/S;
|
||||
x=F*x+K*(obs -H*x); %State estimate
|
||||
Temp=F-K*H;
|
||||
P=Temp*P*Temp';
|
||||
P=P+Q+K*R*K';%MSE estimate
|
||||
end
|
||||
|
|
@ -107,6 +107,12 @@ if ~options_.noprint
|
|||
headers = char('Variables',labels);
|
||||
lh = size(labels,2)+2;
|
||||
dyntable(my_title,headers,labels,M_.Sigma_e,lh,10,6);
|
||||
if options_.TeX
|
||||
labels = deblank(M_.exo_names_tex);
|
||||
headers = char('Variables',labels);
|
||||
lh = size(labels,2)+2;
|
||||
dyn_latex_table(M_,my_title,'covar_ex_shocks',headers,labels,M_.Sigma_e,lh,10,6);
|
||||
end
|
||||
if options_.partial_information
|
||||
skipline()
|
||||
disp('SOLUTION UNDER PARTIAL INFORMATION')
|
||||
|
|
@ -157,10 +163,10 @@ if options_.nomoments == 0
|
|||
elseif options_.periods == 0
|
||||
% There is no code for theoretical moments at 3rd order
|
||||
if options_.order <= 2
|
||||
disp_th_moments(oo_.dr,var_list);
|
||||
oo_=disp_th_moments(oo_.dr,var_list,M_,options_,oo_);
|
||||
end
|
||||
else
|
||||
disp_moments(oo_.endo_simul,var_list);
|
||||
oo_=disp_moments(oo_.endo_simul,var_list,M_,options_,oo_);
|
||||
end
|
||||
end
|
||||
|
||||
|
|
@ -350,7 +356,7 @@ if options_.irf
|
|||
end
|
||||
|
||||
if options_.SpectralDensity.trigger == 1
|
||||
[omega,f] = UnivariateSpectralDensity(oo_.dr,var_list);
|
||||
[oo_] = UnivariateSpectralDensity(M_,oo_,options_,var_list);
|
||||
end
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -1,8 +1,8 @@
|
|||
function [Gamma_y,stationary_vars] = th_autocovariances(dr,ivar,M_,options_,nodecomposition)
|
||||
% Computes the theoretical auto-covariances, Gamma_y, for an AR(p) process
|
||||
% with coefficients dr.ghx and dr.ghu and shock variances Sigma_e_
|
||||
% for a subset of variables ivar (indices in lgy_)
|
||||
% Theoretical HP-filtering is available as an option
|
||||
% with coefficients dr.ghx and dr.ghu and shock variances Sigma_e
|
||||
% for a subset of variables ivar.
|
||||
% Theoretical HP-filtering and band-pass filtering is available as an option
|
||||
%
|
||||
% INPUTS
|
||||
% dr: [structure] Reduced form solution of the DSGE model (decisions rules)
|
||||
|
|
@ -156,7 +156,7 @@ if options_.order == 2 || options_.hp_filter == 0
|
|||
end
|
||||
end
|
||||
end
|
||||
if options_.hp_filter == 0
|
||||
if options_.hp_filter == 0 && ~options_.bandpass.indicator
|
||||
v = NaN*ones(nvar,nvar);
|
||||
v(stationary_vars,stationary_vars) = aa*vx*aa'+ bb*M_.Sigma_e*bb';
|
||||
k = find(abs(v) < 1e-12);
|
||||
|
|
@ -207,37 +207,44 @@ if options_.hp_filter == 0
|
|||
end
|
||||
end
|
||||
end
|
||||
else% ==> Theoretical HP filter.
|
||||
else% ==> Theoretical filters.
|
||||
% 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,:);
|
||||
aa = ghx(iky,:); %R in Uhlig (2001)
|
||||
bb = ghu(iky,:); %S in Uhlig (2001)
|
||||
|
||||
lambda = options_.hp_filter;
|
||||
ngrid = options_.hp_ngrid;
|
||||
freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid));
|
||||
tpos = exp( sqrt(-1)*freqs);
|
||||
tneg = exp(-sqrt(-1)*freqs);
|
||||
hp1 = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
|
||||
mathp_col = [];
|
||||
freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid)); %[0,2*pi)
|
||||
tpos = exp( sqrt(-1)*freqs); %positive frequencies
|
||||
tneg = exp(-sqrt(-1)*freqs); %negative frequencies
|
||||
if options_.bandpass.indicator
|
||||
filter_gain = zeros(1,ngrid);
|
||||
lowest_periodicity=options_.bandpass.passband(2);
|
||||
highest_periodicity=options_.bandpass.passband(1);
|
||||
highest_periodicity=max(2,highest_periodicity); % restrict to upper bound of pi
|
||||
filter_gain(freqs>=2*pi/lowest_periodicity & freqs<=2*pi/highest_periodicity)=1;
|
||||
filter_gain(freqs<=-2*pi/lowest_periodicity+2*pi & freqs>=-2*pi/highest_periodicity+2*pi)=1;
|
||||
else
|
||||
filter_gain = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2); %HP transfer function
|
||||
end
|
||||
mathp_col = NaN(ngrid,length(ivar)^2);
|
||||
IA = eye(size(A,1));
|
||||
IE = eye(M_.exo_nbr);
|
||||
for ig = 1:ngrid
|
||||
if hp1(ig)==0,
|
||||
if filter_gain(ig)==0,
|
||||
f_hp = zeros(length(ivar),length(ivar));
|
||||
else
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*ghu1;IE]...
|
||||
*M_.Sigma_e*[ghu1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
f_omega =(1/(2*pi))*([(IA-A*tneg(ig))\ghu1;IE]...
|
||||
*M_.Sigma_e*[ghu1'/(IA-A'*tpos(ig)) IE]); % spectral density of state variables; top formula Uhlig (2001), p. 20 with N=0
|
||||
g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % spectral density of selected variables; middle formula Uhlig (2001), p. 20; only middle block, i.e. y_t'
|
||||
f_hp = filter_gain(ig)^2*g_omega; % spectral density of selected filtered series; top formula Uhlig (2001), p. 21;
|
||||
end
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
mathp_col(ig,:) = (f_hp(:))'; % store as matrix row for ifft
|
||||
end;
|
||||
% Covariance of filtered series
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi); % Inverse Fast Fourier Transformation; middle formula Uhlig (2001), p. 21;
|
||||
Gamma_y{1} = reshape(imathp_col(1,:),nvar,nvar);
|
||||
% Autocorrelations
|
||||
if nar > 0
|
||||
|
|
@ -253,44 +260,40 @@ else% ==> Theoretical HP filter.
|
|||
Gamma_y{nar+2} = ones(nvar,1);
|
||||
else
|
||||
Gamma_y{nar+2} = zeros(nvar,M_.exo_nbr);
|
||||
SS(exo_names_orig_ord,exo_names_orig_ord) = M_.Sigma_e+1e-14*eye(M_.exo_nbr);
|
||||
SS(exo_names_orig_ord,exo_names_orig_ord) = M_.Sigma_e+1e-14*eye(M_.exo_nbr); %make sure Covariance matrix is positive definite
|
||||
cs = chol(SS)';
|
||||
SS = cs*cs';
|
||||
b1(:,exo_names_orig_ord) = ghu1;
|
||||
b2(:,exo_names_orig_ord) = ghu(iky,:);
|
||||
mathp_col = [];
|
||||
mathp_col = NaN(ngrid,length(ivar)^2);
|
||||
IA = eye(size(A,1));
|
||||
IE = eye(M_.exo_nbr);
|
||||
for ig = 1:ngrid
|
||||
if hp1(ig)==0,
|
||||
if filter_gain(ig)==0,
|
||||
f_hp = zeros(length(ivar),length(ivar));
|
||||
else
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*b1;IE]...
|
||||
*SS*[b1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
f_omega =(1/(2*pi))*( [(IA-A*tneg(ig))\b1;IE]...
|
||||
*SS*[b1'/(IA-A'*tpos(ig)) IE]); % spectral density of state variables; top formula Uhlig (2001), p. 20 with N=0
|
||||
g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % spectral density of selected variables; middle formula Uhlig (2001), p. 20; only middle block, i.e. y_t'
|
||||
f_hp = filter_gain(ig)^2*g_omega; % spectral density of selected filtered series; top formula Uhlig (2001), p. 21;
|
||||
end
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
mathp_col(ig,:) = (f_hp(:))'; % store as matrix row for ifft
|
||||
end;
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
vv = diag(reshape(imathp_col(1,:),nvar,nvar));
|
||||
for i=1:M_.exo_nbr
|
||||
mathp_col = [];
|
||||
mathp_col = NaN(ngrid,length(ivar)^2);
|
||||
SSi = cs(:,i)*cs(:,i)';
|
||||
for ig = 1:ngrid
|
||||
if hp1(ig)==0,
|
||||
if filter_gain(ig)==0,
|
||||
f_hp = zeros(length(ivar),length(ivar));
|
||||
else
|
||||
f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*b1;IE]...
|
||||
*SSi*[b1'*inv(IA-A'*tpos(ig)) ...
|
||||
IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
f_omega =(1/(2*pi))*( [(IA-A*tneg(ig))\b1;IE]...
|
||||
*SSi*[b1'/(IA-A'*tpos(ig)) IE]); % spectral density of state variables; top formula Uhlig (2001), p. 20 with N=0
|
||||
g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % spectral density of selected variables; middle formula Uhlig (2001), p. 20; only middle block, i.e. y_t'
|
||||
f_hp = filter_gain(ig)^2*g_omega; % spectral density of selected filtered series; top formula Uhlig (2001), p. 21;
|
||||
end
|
||||
mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
|
||||
% for ifft
|
||||
mathp_col(ig,:) = (f_hp(:))'; % store as matrix row for ifft
|
||||
end;
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
Gamma_y{nar+2}(:,i) = abs(diag(reshape(imathp_col(1,:),nvar,nvar)))./vv;
|
||||
|
|
|
|||
|
|
@ -7,6 +7,11 @@ MODFILES = \
|
|||
estimation/MH_recover/fs2000_recover.mod \
|
||||
estimation/t_proposal/fs2000_student.mod \
|
||||
estimation/TaRB/fs2000_tarb.mod \
|
||||
moments/example1_var_decomp.mod \
|
||||
moments/example1_hp_test.mod \
|
||||
moments/example1_bp_test.mod \
|
||||
moments/test_AR1_spectral_density.mod \
|
||||
moments/example1_one_sided_hp_test.mod \
|
||||
gsa/ls2003.mod \
|
||||
gsa/ls2003a.mod \
|
||||
gsa/cod_ML_morris/cod_ML_morris.mod \
|
||||
|
|
|
|||
|
|
@ -123,7 +123,8 @@ end;
|
|||
|
||||
steady;
|
||||
|
||||
stoch_simul(order=1,irf=20,graph_format=eps,contemporaneous_correlation);
|
||||
stoch_simul(order=1,irf=20,graph_format=eps,periods=1000,contemporaneous_correlation,conditional_variance_decomposition=[1,3]);
|
||||
stoch_simul(order=1,irf=20,graph_format=eps,periods=0,contemporaneous_correlation,conditional_variance_decomposition=[1,3]);
|
||||
|
||||
write_latex_original_model;
|
||||
write_latex_static_model;
|
||||
|
|
|
|||
|
|
@ -0,0 +1,116 @@
|
|||
/*
|
||||
* Example 1 from F. Collard (2001): "Stochastic simulations with DYNARE:
|
||||
* A practical guide" (see "guide.pdf" in the documentation directory).
|
||||
*/
|
||||
|
||||
/*
|
||||
* Copyright (C) 2001-2010 Dynare Team
|
||||
*
|
||||
* This file is part of Dynare.
|
||||
*
|
||||
* Dynare is free software: you can redistribute it and/or modify
|
||||
* it under the terms of the GNU General Public License as published by
|
||||
* the Free Software Foundation, either version 3 of the License, or
|
||||
* (at your option) any later version.
|
||||
*
|
||||
* Dynare is distributed in the hope that it will be useful,
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
* GNU General Public License for more details.
|
||||
*
|
||||
* You should have received a copy of the GNU General Public License
|
||||
* along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
*/
|
||||
|
||||
|
||||
var y, c, k, a, h, b;
|
||||
varexo e, u;
|
||||
|
||||
parameters beta, rho, alpha, delta, theta, psi, tau;
|
||||
|
||||
alpha = 0.36;
|
||||
rho = 0.95;
|
||||
tau = 0.025;
|
||||
beta = 0.99;
|
||||
delta = 0.025;
|
||||
psi = 0;
|
||||
theta = 2.95;
|
||||
|
||||
phi = 0.1;
|
||||
|
||||
model;
|
||||
c*theta*h^(1+psi)=(1-alpha)*y;
|
||||
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
|
||||
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
|
||||
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
|
||||
k = exp(b)*(y-c)+(1-delta)*k(-1);
|
||||
a = rho*a(-1)+tau*b(-1) + e;
|
||||
b = tau*a(-1)+rho*b(-1) + u;
|
||||
end;
|
||||
|
||||
initval;
|
||||
y = 1.08068253095672;
|
||||
c = 0.80359242014163;
|
||||
h = 0.29175631001732;
|
||||
k = 11.08360443260358;
|
||||
a = 0;
|
||||
b = 0;
|
||||
e = 0;
|
||||
u = 0;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.009;
|
||||
var u; stderr 0.009;
|
||||
var e, u = phi*0.009*0.009;
|
||||
end;
|
||||
|
||||
steady(solve_algo=4,maxit=1000);
|
||||
|
||||
stoch_simul(order=1,nofunctions,irf=0,bandpass_filter=[6 32],hp_ngrid=8192);
|
||||
oo_filtered_all_shocks_theoretical=oo_;
|
||||
|
||||
stoch_simul(order=1,nofunctions,periods=1000000);
|
||||
oo_filtered_all_shocks_simulated=oo_;
|
||||
|
||||
|
||||
shocks;
|
||||
var e; stderr 0;
|
||||
var u; stderr 0.009;
|
||||
var e, u = phi*0.009*0;
|
||||
end;
|
||||
|
||||
stoch_simul(order=1,nofunctions,irf=0,periods=0);
|
||||
|
||||
oo_filtered_one_shock_theoretical=oo_;
|
||||
|
||||
stoch_simul(order=1,nofunctions,periods=5000000);
|
||||
oo_filtered_one_shock_simulated=oo_;
|
||||
|
||||
|
||||
if max(abs((1-diag(oo_filtered_one_shock_simulated.var)./(diag(oo_filtered_all_shocks_simulated.var)))*100-oo_filtered_all_shocks_theoretical.variance_decomposition(:,1)))>2
|
||||
error('Variance Decomposition wrong')
|
||||
end
|
||||
|
||||
if max(max(abs(oo_filtered_all_shocks_simulated.var-oo_filtered_all_shocks_theoretical.var)))>2e-4;
|
||||
error('Covariance wrong')
|
||||
end
|
||||
|
||||
if max(max(abs(oo_filtered_one_shock_simulated.var-oo_filtered_one_shock_theoretical.var)))>1e-4;
|
||||
error('Covariance wrong')
|
||||
end
|
||||
|
||||
for ii=1:options_.ar
|
||||
autocorr_model_all_shocks_simulated(:,ii)=diag(oo_filtered_all_shocks_simulated.autocorr{ii});
|
||||
autocorr_model_all_shocks_theoretical(:,ii)=diag(oo_filtered_all_shocks_theoretical.autocorr{ii});
|
||||
autocorr_model_one_shock_simulated(:,ii)=diag(oo_filtered_one_shock_simulated.autocorr{ii});
|
||||
autocorr_model_one_shock_theoretical(:,ii)=diag(oo_filtered_one_shock_theoretical.autocorr{ii});
|
||||
end
|
||||
|
||||
if max(max(abs(autocorr_model_all_shocks_simulated-autocorr_model_all_shocks_theoretical)))>2e-2;
|
||||
error('Correlation wrong')
|
||||
end
|
||||
|
||||
if max(max(abs(autocorr_model_one_shock_simulated-autocorr_model_one_shock_theoretical)))>2e-2;
|
||||
error('Correlation wrong')
|
||||
end
|
||||
|
|
@ -0,0 +1,159 @@
|
|||
/*
|
||||
* Example 1 from F. Collard (2001): "Stochastic simulations with DYNARE:
|
||||
* A practical guide" (see "guide.pdf" in the documentation directory).
|
||||
*/
|
||||
|
||||
/*
|
||||
* Copyright (C) 2001-2010 Dynare Team
|
||||
*
|
||||
* This file is part of Dynare.
|
||||
*
|
||||
* Dynare is free software: you can redistribute it and/or modify
|
||||
* it under the terms of the GNU General Public License as published by
|
||||
* the Free Software Foundation, either version 3 of the License, or
|
||||
* (at your option) any later version.
|
||||
*
|
||||
* Dynare is distributed in the hope that it will be useful,
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
* GNU General Public License for more details.
|
||||
*
|
||||
* You should have received a copy of the GNU General Public License
|
||||
* along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
*/
|
||||
|
||||
|
||||
var y, c, k, a, h, b;
|
||||
varexo e, u;
|
||||
|
||||
parameters beta, rho, alpha, delta, theta, psi, tau;
|
||||
|
||||
alpha = 0.36;
|
||||
rho = 0.95;
|
||||
tau = 0.025;
|
||||
beta = 0.99;
|
||||
delta = 0.025;
|
||||
psi = 0;
|
||||
theta = 2.95;
|
||||
|
||||
phi = 0.1;
|
||||
|
||||
model;
|
||||
c*theta*h^(1+psi)=(1-alpha)*y;
|
||||
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
|
||||
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
|
||||
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
|
||||
k = exp(b)*(y-c)+(1-delta)*k(-1);
|
||||
a = rho*a(-1)+tau*b(-1) + e;
|
||||
b = tau*a(-1)+rho*b(-1) + u;
|
||||
end;
|
||||
|
||||
initval;
|
||||
y = 1.08068253095672;
|
||||
c = 0.80359242014163;
|
||||
h = 0.29175631001732;
|
||||
k = 11.08360443260358;
|
||||
a = 0;
|
||||
b = 0;
|
||||
e = 0;
|
||||
u = 0;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.009;
|
||||
var u; stderr 0.009;
|
||||
var e, u = phi*0.009*0.009;
|
||||
end;
|
||||
|
||||
steady(solve_algo=4,maxit=1000);
|
||||
options_.hp_ngrid=2048*4;
|
||||
options_.bandpass.indicator=0;
|
||||
options_.bandpass.passband=[6 32];
|
||||
|
||||
stoch_simul(order=1,nofunctions,hp_filter=1600,irf=0);
|
||||
|
||||
total_var_filtered=diag(oo_.var);
|
||||
oo_filtered_all_shocks=oo_;
|
||||
|
||||
stoch_simul(order=1,nofunctions,hp_filter=0,periods=5000000,nomoments);
|
||||
options_.nomoments=0;
|
||||
oo_unfiltered_all_shocks=oo_;
|
||||
|
||||
[junk, y_filtered]=sample_hp_filter(y,1600);
|
||||
[junk, c_filtered]=sample_hp_filter(c,1600);
|
||||
[junk, k_filtered]=sample_hp_filter(k,1600);
|
||||
[junk, a_filtered]=sample_hp_filter(a,1600);
|
||||
[junk, h_filtered]=sample_hp_filter(h,1600);
|
||||
[junk, b_filtered]=sample_hp_filter(b,1600);
|
||||
|
||||
verbatim;
|
||||
total_std_all_shocks_filtered_sim=std([y_filtered c_filtered k_filtered a_filtered h_filtered b_filtered])
|
||||
cov_filtered_all_shocks=cov([y_filtered c_filtered k_filtered a_filtered h_filtered b_filtered])
|
||||
acf = zeros(6);
|
||||
[junk, acf(:,1)] = sample_autocovariance([y_filtered ],5);
|
||||
[junk, acf(:,2)] = sample_autocovariance([c_filtered ],5);
|
||||
[junk, acf(:,3)] = sample_autocovariance([k_filtered ],5);
|
||||
[junk, acf(:,4)] = sample_autocovariance([a_filtered ],5);
|
||||
[junk, acf(:,5)] = sample_autocovariance([h_filtered ],5);
|
||||
[junk, acf(:,6)] = sample_autocovariance([b_filtered ],5);
|
||||
autocorr_filtered_all_shocks=acf(2:end,:)';
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0;
|
||||
var u; stderr 0.009;
|
||||
var e, u = phi*0.009*0;
|
||||
end;
|
||||
|
||||
stoch_simul(order=1,nofunctions,hp_filter=1600,irf=0,periods=0);
|
||||
|
||||
total_var_filtered_one_shock=diag(oo_.var);
|
||||
oo_filtered_one_shock=oo_;
|
||||
|
||||
stoch_simul(order=1,nofunctions,hp_filter=0,periods=5000000,nomoments);
|
||||
oo_unfiltered_one_shock=oo_;
|
||||
|
||||
[junk, y_filtered]=sample_hp_filter(y,1600);
|
||||
[junk, c_filtered]=sample_hp_filter(c,1600);
|
||||
[junk, k_filtered]=sample_hp_filter(k,1600);
|
||||
[junk, a_filtered]=sample_hp_filter(a,1600);
|
||||
[junk, h_filtered]=sample_hp_filter(h,1600);
|
||||
[junk, b_filtered]=sample_hp_filter(b,1600);
|
||||
|
||||
verbatim;
|
||||
total_std_one_shock_filtered_sim=std([y_filtered c_filtered k_filtered a_filtered h_filtered b_filtered])
|
||||
cov_filtered_one_shock=cov([y_filtered c_filtered k_filtered a_filtered h_filtered b_filtered])
|
||||
acf = zeros(6);
|
||||
[junk, acf(:,1)] = sample_autocovariance([y_filtered ],5);
|
||||
[junk, acf(:,2)] = sample_autocovariance([c_filtered ],5);
|
||||
[junk, acf(:,3)] = sample_autocovariance([k_filtered ],5);
|
||||
[junk, acf(:,4)] = sample_autocovariance([a_filtered ],5);
|
||||
[junk, acf(:,5)] = sample_autocovariance([h_filtered ],5);
|
||||
[junk, acf(:,6)] = sample_autocovariance([b_filtered ],5);
|
||||
autocorr_filtered_one_shock=acf(2:end,:)';
|
||||
end;
|
||||
|
||||
if max(abs((1-(total_std_one_shock_filtered_sim.^2)./(total_std_all_shocks_filtered_sim.^2))*100-oo_filtered_all_shocks.variance_decomposition(:,1)'))>2
|
||||
error('Variance Decomposition wrong')
|
||||
end
|
||||
|
||||
if max(max(abs(oo_filtered_all_shocks.var-cov_filtered_all_shocks)))>1e-4;
|
||||
error('Covariance wrong')
|
||||
end
|
||||
|
||||
if max(max(abs(oo_filtered_one_shock.var-cov_filtered_one_shock)))>5e-5;
|
||||
error('Covariance wrong')
|
||||
end
|
||||
|
||||
for ii=1:options_.ar
|
||||
autocorr_model_all_shocks(:,ii)=diag(oo_filtered_all_shocks.autocorr{ii});
|
||||
autocorr_model_one_shock(:,ii)=diag(oo_filtered_one_shock.autocorr{ii});
|
||||
end
|
||||
|
||||
if max(max(abs(autocorr_model_all_shocks-autocorr_filtered_all_shocks)))>1e-2;
|
||||
error('Covariance wrong')
|
||||
end
|
||||
|
||||
if max(max(abs(autocorr_model_one_shock-autocorr_filtered_one_shock)))>1e-2;
|
||||
error('Covariance wrong')
|
||||
end
|
||||
|
|
@ -0,0 +1,71 @@
|
|||
/*
|
||||
* Example 1 from F. Collard (2001): "Stochastic simulations with DYNARE:
|
||||
* A practical guide" (see "guide.pdf" in the documentation directory).
|
||||
*/
|
||||
|
||||
/*
|
||||
* Copyright (C) 2001-2010 Dynare Team
|
||||
*
|
||||
* This file is part of Dynare.
|
||||
*
|
||||
* Dynare is free software: you can redistribute it and/or modify
|
||||
* it under the terms of the GNU General Public License as published by
|
||||
* the Free Software Foundation, either version 3 of the License, or
|
||||
* (at your option) any later version.
|
||||
*
|
||||
* Dynare is distributed in the hope that it will be useful,
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
* GNU General Public License for more details.
|
||||
*
|
||||
* You should have received a copy of the GNU General Public License
|
||||
* along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
*/
|
||||
|
||||
|
||||
var y, c, k, a, h, b;
|
||||
varexo e, u;
|
||||
|
||||
parameters beta, rho, alpha, delta, theta, psi, tau;
|
||||
|
||||
alpha = 0.36;
|
||||
rho = 0.95;
|
||||
tau = 0.025;
|
||||
beta = 0.99;
|
||||
delta = 0.025;
|
||||
psi = 0;
|
||||
theta = 2.95;
|
||||
|
||||
phi = 0.1;
|
||||
|
||||
model;
|
||||
c*theta*h^(1+psi)=(1-alpha)*y;
|
||||
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
|
||||
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
|
||||
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
|
||||
k = exp(b)*(y-c)+(1-delta)*k(-1);
|
||||
a = rho*a(-1)+tau*b(-1) + e;
|
||||
b = tau*a(-1)+rho*b(-1) + u;
|
||||
end;
|
||||
|
||||
initval;
|
||||
y = 1.08068253095672;
|
||||
c = 0.80359242014163;
|
||||
h = 0.29175631001732;
|
||||
k = 11.08360443260358;
|
||||
a = 0;
|
||||
b = 0;
|
||||
e = 0;
|
||||
u = 0;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.009;
|
||||
var u; stderr 0.009;
|
||||
var e, u = phi*0.009*0.009;
|
||||
end;
|
||||
|
||||
steady(solve_algo=4,maxit=1000);
|
||||
options_.hp_ngrid=2048*4;
|
||||
|
||||
stoch_simul(order=1,nofunctions,one_sided_hp_filter=1600,irf=0,periods=5000);
|
||||
|
|
@ -0,0 +1,89 @@
|
|||
/*
|
||||
* Example 1 from F. Collard (2001): "Stochastic simulations with DYNARE:
|
||||
* A practical guide" (see "guide.pdf" in the documentation directory).
|
||||
*/
|
||||
|
||||
/*
|
||||
* Copyright (C) 2001-2010 Dynare Team
|
||||
*
|
||||
* This file is part of Dynare.
|
||||
*
|
||||
* Dynare is free software: you can redistribute it and/or modify
|
||||
* it under the terms of the GNU General Public License as published by
|
||||
* the Free Software Foundation, either version 3 of the License, or
|
||||
* (at your option) any later version.
|
||||
*
|
||||
* Dynare is distributed in the hope that it will be useful,
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
* GNU General Public License for more details.
|
||||
*
|
||||
* You should have received a copy of the GNU General Public License
|
||||
* along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
*/
|
||||
|
||||
|
||||
var y, c, k, a, h, b;
|
||||
varexo e, u, junk;
|
||||
|
||||
parameters beta, rho, alpha, delta, theta, psi, tau;
|
||||
|
||||
alpha = 0.36;
|
||||
rho = 0.95;
|
||||
tau = 0.025;
|
||||
beta = 0.99;
|
||||
delta = 0.025;
|
||||
psi = 0;
|
||||
theta = 2.95;
|
||||
|
||||
phi = 0;
|
||||
|
||||
model;
|
||||
c*theta*h^(1+psi)=(1-alpha)*y;
|
||||
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
|
||||
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
|
||||
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
|
||||
k = exp(b)*(y-c)+(1-delta)*k(-1);
|
||||
a = rho*a(-1)+tau*b(-1) + e;
|
||||
b = tau*a(-1)+rho*b(-1) + u;
|
||||
end;
|
||||
|
||||
initval;
|
||||
y = 1.08068253095672;
|
||||
c = 0.80359242014163;
|
||||
h = 0.29175631001732;
|
||||
k = 11.08360443260358;
|
||||
a = 0;
|
||||
b = 0;
|
||||
e = 0;
|
||||
u = 0;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.009;
|
||||
var u; stderr 0.009;
|
||||
var e, u = phi*0.009*0.009;
|
||||
end;
|
||||
|
||||
stoch_simul(relative_irf,order=1,periods=0);
|
||||
oo_1_theoretic=oo_;
|
||||
stoch_simul(relative_irf,order=1,periods=100000);
|
||||
oo_1_simul=oo_;
|
||||
stoch_simul(relative_irf,order=2,periods=0);
|
||||
oo_2_theoretic=oo_;
|
||||
set_dynare_seed('default');
|
||||
stoch_simul(relative_irf,order=2,periods=100000);
|
||||
oo_2_simul=oo_;
|
||||
|
||||
if max(max(abs(oo_1_theoretic.variance_decomposition-oo_1_simul.variance_decomposition)))>2
|
||||
error('Variance Decomposition wrong')
|
||||
end
|
||||
|
||||
if max(max(abs(oo_1_theoretic.variance_decomposition-oo_2_theoretic.variance_decomposition)))>1e-10
|
||||
error('Theoretical Variance Decomposition wrong')
|
||||
end
|
||||
|
||||
if max(max(abs(oo_2_theoretic.variance_decomposition-oo_2_simul.variance_decomposition)))>3
|
||||
error('Variance Decomposition wrong')
|
||||
end
|
||||
|
||||
|
|
@ -0,0 +1,76 @@
|
|||
var white_noise ar1;
|
||||
varexo e;
|
||||
|
||||
parameters phi;
|
||||
|
||||
phi=0.9;
|
||||
|
||||
model;
|
||||
white_noise=e;
|
||||
ar1=phi*ar1(-1)+e;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e = 1;
|
||||
end;
|
||||
|
||||
options_.SpectralDensity.trigger=1;
|
||||
|
||||
options_.bandpass.indicator=0;
|
||||
options_.hp_ngrid=2048;
|
||||
|
||||
stoch_simul(order=1,nofunctions,hp_filter=0,irf=0,periods=1000000);
|
||||
|
||||
white_noise_sample=white_noise;
|
||||
|
||||
theoretical_spectrum_white_noise=1^2/(2*pi); %Hamilton (1994), 6.1.9
|
||||
if max(abs(oo_.SpectralDensity.density(strmatch('white_noise',M_.endo_names,'exact'),:)-theoretical_spectrum_white_noise))>1e-10
|
||||
error('Spectral Density is wrong')
|
||||
end
|
||||
|
||||
theoretical_spectrum_AR1=1/(2*pi)*(1^2./(1+phi^2-2*phi*cos(oo_.SpectralDensity.freqs))); %Hamilton (1994), 6.1.13
|
||||
if max(abs(oo_.SpectralDensity.density(strmatch('ar1',M_.endo_names,'exact'),:)-theoretical_spectrum_AR1'))>1e-10
|
||||
error('Spectral Density is wrong')
|
||||
end
|
||||
|
||||
stoch_simul(order=1,nofunctions,hp_filter=1600,irf=0,periods=0);
|
||||
lambda=options_.hp_filter;
|
||||
Kalman_gain=(4*lambda*(1 - cos(oo_.SpectralDensity.freqs)).^2 ./ (1 + 4*lambda*(1 - cos(oo_.SpectralDensity.freqs)).^2));
|
||||
theoretical_spectrum_white_noise_hp_filtered=1^2/(2*pi)*Kalman_gain.^2; %Hamilton (1994), 6.1.9
|
||||
if max(abs(oo_.SpectralDensity.density(strmatch('white_noise',M_.endo_names,'exact'),:)-theoretical_spectrum_white_noise_hp_filtered'))>1e-10
|
||||
error('Spectral Density is wrong')
|
||||
end
|
||||
|
||||
theoretical_spectrum_AR1_hp_filtered=1/(2*pi)*(1^2./(1+phi^2-2*phi*cos(oo_.SpectralDensity.freqs))).*Kalman_gain.^2; %Hamilton (1994), 6.1.13
|
||||
if max(abs(oo_.SpectralDensity.density(strmatch('ar1',M_.endo_names,'exact'),:)-theoretical_spectrum_AR1_hp_filtered'))>1e-10
|
||||
error('Spectral Density is wrong')
|
||||
end
|
||||
|
||||
options_.hp_filter=0;
|
||||
stoch_simul(order=1,nofunctions,bandpass_filter=[6 32],irf=0);
|
||||
|
||||
theoretical_spectrum_white_noise=repmat(theoretical_spectrum_white_noise,1,options_.hp_ngrid);
|
||||
passband=oo_.SpectralDensity.freqs>=2*pi/options_.bandpass.passband(2) & oo_.SpectralDensity.freqs<=2*pi/options_.bandpass.passband(1);
|
||||
if max(abs(oo_.SpectralDensity.density(strmatch('white_noise',M_.endo_names,'exact'),passband)-theoretical_spectrum_white_noise(passband)))>1e-10
|
||||
error('Spectral Density is wrong')
|
||||
end
|
||||
if max(abs(oo_.SpectralDensity.density(strmatch('white_noise',M_.endo_names,'exact'),~passband)-0))>1e-10
|
||||
error('Spectral Density is wrong')
|
||||
end
|
||||
|
||||
if max(abs(oo_.SpectralDensity.density(strmatch('ar1',M_.endo_names,'exact'),passband)-theoretical_spectrum_AR1(passband)'))>1e-10
|
||||
error('Spectral Density is wrong')
|
||||
end
|
||||
if max(abs(oo_.SpectralDensity.density(strmatch('ar1',M_.endo_names,'exact'),~passband)-0))>1e-10
|
||||
error('Spectral Density is wrong')
|
||||
end
|
||||
|
||||
|
||||
% [pow,f]=psd(a_sample,1024,1,[],512);
|
||||
% figure
|
||||
% plot(f,pow/(2*pi))
|
||||
%
|
||||
% % figure
|
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% % [pow,f]=psd(a_sample,1000,1,[],500);
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% % plot(f(3:end)*2*pi,pow(3:end)/(2*pi));
|
||||
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Reference in New Issue