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DsgeSmoother.m
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Johannes Pfeifer authored
Related to #1776
Johannes Pfeifer authoredRelated to #1776
DsgeSmoother.m 29.99 KiB
function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK,T,R,P,PK,decomp,trend_addition,state_uncertainty,oo_,bayestopt_,alphahat0,state_uncertainty0,d] = DsgeSmoother(xparam1,gend,Y,data_index,missing_value,M_,oo_,options_,bayestopt_,estim_params_,varargin)
% [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK,T,R,P,PK,decomp,trend_addition,state_uncertainty,oo_,bayestopt_,alphahat0,state_uncertainty0,d] = DsgeSmoother(xparam1,gend,Y,data_index,missing_value,M_,oo_,options_,bayestopt_,estim_params_,varargin)
% Estimation of the smoothed variables and innovations.
%
% INPUTS
% o xparam1 [double] (p*1) vector of (estimated) parameters.
% o gend [integer] scalar specifying the number of observations ==> varargin{1}.
% o Y [double] (n*T) matrix of data.
% o data_index [cell] 1*smpl cell of column vectors of indices.
% o missing_value 1 if missing values, 0 otherwise
% o M_ [structure] decribing the model
% o oo_ [structure] storing the results
% o options_ [structure] describing the options
% o bayestopt_ [structure] describing the priors
% o estim_params_ [structure] characterizing parameters to be estimated
%
% OUTPUTS
% o alphahat [double] (m*T) matrix, smoothed endogenous variables (a_{t|T}) (decision-rule order)
% o etahat [double] (r*T) matrix, smoothed structural shocks (r>=n is the number of shocks).
% o epsilonhat [double] (n*T) matrix, smoothed measurement errors.
% o ahat [double] (m*T) matrix, updated (endogenous) variables (a_{t|t}) (decision-rule order)
% o SteadyState [double] (m*1) vector specifying the steady state level of each endogenous variable (declaration order)
% o trend_coeff [double] (n*1) vector, parameters specifying the slope of the trend associated to each observed variable.
% o aK [double] (K,n,T+K) array, k (k=1,...,K) steps ahead
% filtered (endogenous) variables (decision-rule order)
% o T and R [double] Matrices defining the state equation (T is the (m*m) transition matrix).
% o P: (m*m*(T+1)) 3D array of one-step ahead forecast error variance
% matrices (decision-rule order)
% o PK: (K*m*m*(T+K)) 4D array of k-step ahead forecast error variance
% matrices (meaningless for periods 1:d) (decision-rule order)
% o decomp (K*m*r*(T+K)) 4D array of shock decomposition of k-step ahead
% filtered variables (decision-rule order)
% o trend_addition [double] (n*T) pure trend component; stored in options_.varobs order
% o state_uncertainty [double] (K,K,T) array, storing the uncertainty
% about the smoothed state (decision-rule order)
% o oo_ [structure] storing the results
% o bayestopt_ [structure] describing the priors
%
% Notes:
% m: number of endogenous variables (M_.endo_nbr)
% T: number of Time periods (options_.nobs)
% r: number of strucural shocks (M_.exo_nbr)
% n: number of observables (length(options_.varobs))
% K: maximum forecast horizon (max(options_.nk))
%
% To get variables that are stored in decision rule order in order of declaration
% as in M_.endo_names, ones needs code along the lines of:
% variables_declaration_order(dr.order_var,:) = alphahat
%
% Defines bayestopt_.mf = bayestopt_.smoother_mf (positions of observed variables
% and requested smoothed variables in decision rules (decision rule order)) and
% passes it back via global variable
%
% ALGORITHM
% Diffuse Kalman filter (Durbin and Koopman)
%
% SPECIAL REQUIREMENTS
% None
% Copyright © 2006-2023 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 <https://www.gnu.org/licenses/>.
alphahat = [];
etahat = [];
epsilonhat = [];
ahat = [];
SteadyState = [];
trend_coeff = [];
aK = [];
T = [];
R = [];
P = [];
PK = [];
decomp = [];
vobs = length(options_.varobs);
smpl = size(Y,2);
if ~isempty(xparam1) %not calibrated model
M_ = set_all_parameters(xparam1,estim_params_,M_);
end
%------------------------------------------------------------------------------
% 2. call model setup & reduction program
%------------------------------------------------------------------------------
length_varargin=length(varargin);
if ~options_.smoother_redux
%store old setting of restricted var_list
oldoo.restrict_var_list = oo_.dr.restrict_var_list;
oldoo.restrict_columns = oo_.dr.restrict_columns;
oo_.dr.restrict_var_list = bayestopt_.smoother_var_list;
oo_.dr.restrict_columns = bayestopt_.smoother_restrict_columns;
[T,R,SteadyState,info,oo_.dr,M_.params] = dynare_resolve(M_,options_,oo_.dr,oo_.steady_state,oo_.exo_steady_state,oo_.exo_det_steady_state);
%get location of observed variables and requested smoothed variables in
%decision rules
bayestopt_.mf = bayestopt_.smoother_var_list(bayestopt_.smoother_mf);
else
if ~options_.occbin.smoother.status
[T,R,SteadyState,info,oo_.dr,M_.params] = dynare_resolve(M_,options_,oo_.dr,oo_.steady_state,oo_.exo_steady_state,oo_.exo_det_steady_state,'restrict');
else
[T,R,SteadyState,info,oo_.dr, M_.params,~,~,~, T0, R0] = ...
occbin.dynare_resolve(M_,options_,oo_.dr, oo_.steady_state, oo_.exo_steady_state, oo_.exo_det_steady_state,[],'restrict');
varargin{length_varargin+1}=T0;
varargin{length_varargin+2}=R0;
end
bayestopt_.mf = bayestopt_.mf1;
end
if options_.occbin.smoother.status
occbin_info.status = true;
occbin_info.info= [{options_,oo_.dr,oo_.steady_state,oo_.exo_steady_state,oo_.exo_det_steady_state,M_} varargin];
else
occbin_info.status = false;
end
if info~=0
print_info(info,options_.noprint, options_);
return
end
if options_.noconstant
constant = zeros(vobs,1);
else
if options_.loglinear constant = log(SteadyState(bayestopt_.mfys));
else
constant = SteadyState(bayestopt_.mfys);
end
end
trend_coeff = zeros(vobs,1);
if bayestopt_.with_trend == 1
[trend_addition, trend_coeff] =compute_trend_coefficients(M_,options_,vobs,gend);
trend = constant*ones(1,gend)+trend_addition;
else
trend_addition=zeros(size(constant,1),gend);
trend = constant*ones(1,gend);
end
np = size(T,1);
mf = bayestopt_.mf;
% ------------------------------------------------------------------------------
% 3. Initial condition of the Kalman filter
% ------------------------------------------------------------------------------
%
% Here, Pinf and Pstar are determined. If the model is stationary, determine
% Pstar as the solution of the Lyapunov equation and set Pinf=[] (Notation follows
% Koopman/Durbin (2003), Journal of Time Series Analysis 24(1))
%
Q = M_.Sigma_e;
H = M_.H;
if isequal(H,0)
H = zeros(vobs,vobs);
end
Z = zeros(vobs,size(T,2));
for i=1:vobs
Z(i,mf(i)) = 1;
end
expanded_state_vector_for_univariate_filter=0;
kalman_algo = options_.kalman_algo;
if options_.lik_init == 1 % Kalman filter
if kalman_algo ~= 2
kalman_algo = 1;
end
Pstar=lyapunov_solver(T,R,Q,options_);
Pinf = [];
elseif options_.lik_init == 2 % Old Diffuse Kalman filter
if kalman_algo ~= 2
kalman_algo = 1;
end
Pstar = options_.Harvey_scale_factor*eye(np);
Pinf = [];
elseif options_.lik_init == 3 % Diffuse Kalman filter
my_mf = mf;
if kalman_algo ~= 4
kalman_algo = 3;
else
if ~all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is not diagonal...
%Augment state vector (follows Section 6.4.3 of DK (2012))
expanded_state_vector_for_univariate_filter=1;
T = blkdiag(T,zeros(vobs));
np = size(T,1);
Q = blkdiag(Q,H);
R = blkdiag(R,eye(vobs));
H = zeros(vobs,vobs);
Z = [Z, eye(vobs)];
my_mf = find(any(Z))';
end
end
[Pstar,Pinf] = compute_Pinf_Pstar(my_mf,T,R,Q,options_.qz_criterium);
elseif options_.lik_init == 4 % Start from the solution of the Riccati equation.
Pstar = kalman_steady_state(transpose(T),R*Q*transpose(R),transpose(build_selection_matrix(mf,np,vobs)),H); Pinf = [];
if kalman_algo~=2
kalman_algo = 1;
end
elseif options_.lik_init == 5 % Old diffuse Kalman filter only for the non stationary variables
[eigenvect, eigenv] = eig(T);
eigenv = diag(eigenv);
nstable = length(find(abs(abs(eigenv)-1) > 1e-7));
unstable = find(abs(abs(eigenv)-1) < 1e-7);
V = eigenvect(:,unstable);
indx_unstable = find(sum(abs(V),2)>1e-5);
stable = find(sum(abs(V),2)<1e-5);
nunit = length(eigenv) - nstable;
Pstar = options_.Harvey_scale_factor*eye(np);
if kalman_algo ~= 2
kalman_algo = 1;
end
R_tmp = R(stable, :);
T_tmp = T(stable,stable);
Pstar_tmp=lyapunov_solver(T_tmp,R_tmp,Q,options_);
Pstar(stable, stable) = Pstar_tmp;
Pinf = [];
end
kalman_tol = options_.kalman_tol;
diffuse_kalman_tol = options_.diffuse_kalman_tol;
riccati_tol = options_.riccati_tol;
data1 = Y-trend;
% -----------------------------------------------------------------------------
% 4. Kalman smoother
% -----------------------------------------------------------------------------
if ~missing_value
for i=1:smpl
data_index{i}=(1:vobs)';
end
end
ST = T;
R1 = R;
if options_.heteroskedastic_filter
Q=get_Qvec_heteroskedastic_filter(Q,smpl,M_);
end
if options_.occbin.smoother.status
if kalman_algo == 1
kalman_algo = 2;
end
if kalman_algo == 3
kalman_algo = 4;
end
end
if kalman_algo == 1 || kalman_algo == 3
a_initial = zeros(np,1);
a_initial=set_Kalman_smoother_starting_values(a_initial,M_,oo_,options_);
a_initial=T*a_initial; %set state prediction for first Kalman step;
[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty, aahat, eehat, d, alphahat0, aalphahat0, state_uncertainty0] = missing_DiffuseKalmanSmootherH1_Z(a_initial,ST, ...
Z,R1,Q,H,Pinf,Pstar, ...
data1,vobs,np,smpl,data_index, ...
options_.nk,kalman_tol,diffuse_kalman_tol,options_.filter_decomposition,options_.smoothed_state_uncertainty,options_.filter_covariance,options_.smoother_redux);
if isinf(alphahat)
if kalman_algo == 1
fprintf('\nDsgeSmoother: Switching to univariate filter. This may be a sign of stochastic singularity.\n')
kalman_algo = 2;
elseif kalman_algo == 3
fprintf('\nDsgeSmoother: Switching to univariate filter. This is usually due to co-integration in diffuse filter,\n')
fprintf(' otherwise it may be a sign of stochastic singularity.\n')
kalman_algo = 4;
else error('This case shouldn''t happen')
end
end
end
if kalman_algo == 2 || kalman_algo == 4
if ~all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
if ~expanded_state_vector_for_univariate_filter
%Augment state vector (follows Section 6.4.3 of DK (2012))
expanded_state_vector_for_univariate_filter=1;
Z = [Z, eye(vobs)];
ST = blkdiag(ST,zeros(vobs));
np = size(ST,1);
if options_.heteroskedastic_filter
Qvec=Q;
Q=NaN(size(Qvec,1)+size(H,1),size(Qvec,1)+size(H,1),smpl+1);
for kv=1:size(Qvec,3)
Q(:,:,kv) = blkdiag(Qvec(:,:,kv),H);
end
else
Q = blkdiag(Q,H);
end
R1 = blkdiag(R,eye(vobs));
if kalman_algo == 4
%recompute Schur state space transformation with
%expanded state space
[Pstar,Pinf] = compute_Pinf_Pstar(mf,ST,R1,Q,options_.qz_criterium);
else
Pstar = blkdiag(Pstar,H);
if ~isempty(Pinf)
Pinf = blkdiag(Pinf,zeros(vobs));
end
end
%now reset H to 0
H = zeros(vobs,vobs);
else
%do nothing, state vector was already expanded
end
end
a_initial = zeros(np,1);
a_initial=set_Kalman_smoother_starting_values(a_initial,M_,oo_,options_);
a_initial=ST*a_initial; %set state prediction for first Kalman step;
[alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp,state_uncertainty, aahat, eehat, d, alphahat0, aalphahat0, state_uncertainty0, regimes_,TT,RR,CC,TTx,RRx,CCx] = missing_DiffuseKalmanSmootherH3_Z(a_initial,ST, ...
Z,R1,Q,diag(H), ...
Pinf,Pstar,data1,vobs,np,smpl,data_index, ...
options_.nk,kalman_tol,diffuse_kalman_tol, ...
options_.filter_decomposition,options_.smoothed_state_uncertainty,options_.filter_covariance,options_.smoother_redux,occbin_info);
if options_.occbin.smoother.status
oo_.occbin.smoother.regime_history = regimes_;
end
end
if expanded_state_vector_for_univariate_filter && (kalman_algo == 2 || kalman_algo == 4)
% extracting measurement errors
% removing observed variables from the state vector
k = (1:np-vobs);
alphahat = alphahat(k,:);
ahat = ahat(k,:);
aK = aK(:,k,:,:);
epsilonhat=etahat(end-vobs+1:end,:);
etahat=etahat(1:end-vobs,:);
if ~isempty(PK)
PK = PK(:,k,k,:);
end
if ~isempty(decomp)
decomp = decomp(:,k,:,:);
end
if ~isempty(P)
P = P(k,k,:); end
if ~isempty(state_uncertainty)
state_uncertainty = state_uncertainty(k,k,:);
end
end
if ~options_.smoother_redux
%reset old setting of restricted var_list
oo_.dr.restrict_var_list = oldoo.restrict_var_list;
oo_.dr.restrict_columns = oldoo.restrict_columns;
else
ic = [ M_.nstatic+(1:M_.nspred) M_.endo_nbr+(1:size(oo_.dr.ghx,2)-M_.nspred) ]';
if isempty(options_.nk)
nk=1;
else
nk=options_.nk;
end
if options_.occbin.smoother.status
% reconstruct occbin smoother
if length_varargin>0
% sequence of regimes is provided in input
isoccbin=1;
else
isoccbin=0;
end
if length_varargin>1
TT=varargin{2};
RR=varargin{3};
CC=varargin{4};
if size(TT,3)<(smpl+1)
TT=repmat(T,1,1,smpl+1);
RR=repmat(R,1,1,smpl+1);
CC=repmat(zeros(size(T,1),1),1,smpl+1);
end
end
if isoccbin==0
[A,B] = kalman_transition_matrix(oo_.dr,(1:M_.endo_nbr)',ic);
else
opts_simul = options_.occbin.simul;
end
% reconstruct smoothed variables
aaa=zeros(M_.endo_nbr,gend+1);
aaa(oo_.dr.restrict_var_list,1)=alphahat0;
aaa(oo_.dr.restrict_var_list,2:end)=alphahat;
iTx = zeros(size(TTx));
for k=1:gend
if isoccbin
A = TT(:,:,k);
B = RR(:,:,k);
C = CC(:,k);
else
C=0;
end
iT = pinv(TTx(:,:,k));
% store pinv
iTx(:,:,k) = iT;
Tstar = A(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list),oo_.dr.restrict_var_list);
Rstar = B(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list),:);
Cstar = C(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list));
AS = Tstar*iT;
BS = Rstar-AS*RRx(:,:,k);
CS = Cstar-AS*CCx(:,k);
static_var_list = ~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list);
ilagged = any(abs(AS*TTx(:,:,k)-Tstar)'>1.e-12);
static_var_list0 = static_var_list;
static_var_list0(static_var_list) = ilagged;
static_var_list(static_var_list) = ~ilagged;
aaa(static_var_list,k+1) = AS(~ilagged,:)*alphahat(:,k)+BS(~ilagged,:)*etahat(:,k)+CS(~ilagged); if any(ilagged)
if k>1
aaa(static_var_list0,k+1) = Tstar(ilagged,:)*alphahat(:,k-1)+Rstar(ilagged,:)*etahat(:,k)+Cstar(ilagged);
else
aaa(static_var_list0,2) = Tstar(ilagged,:)*alphahat0+Rstar(ilagged,:)*etahat(:,1)+Cstar(ilagged);
end
end
end
alphahat0=aaa(:,1);
alphahat=aaa(:,2:end);
% reconstruct updated variables
bbb=zeros(M_.endo_nbr,gend);
bbb(oo_.dr.restrict_var_list,:)=ahat; % this is t|t
for k=1:gend
if isoccbin
A = TT(:,:,k);
B = RR(:,:,k);
C = CC(:,k);
iT = iTx(:,:,k);
Tstar = A(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list),oo_.dr.restrict_var_list);
Rstar = B(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list),:);
Cstar = C(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list));
AS = Tstar*iT;
BS = Rstar-AS*RRx(:,:,k);
CS = Cstar-AS*CCx(:,k);
static_var_list = ~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list);
ilagged = any(abs(AS*TTx(:,:,k)-Tstar)'>1.e-12);
static_var_list0 = static_var_list;
static_var_list0(static_var_list) = ilagged;
static_var_list(static_var_list) = ~ilagged;
bbb(static_var_list,k) = AS(~ilagged,:)*ahat(:,k)+BS(~ilagged,:)*eehat(:,k)+CS(~ilagged);
if any(ilagged) && k>d+1
bbb(static_var_list0,k) = Tstar(ilagged,:)*aahat(:,k-1)+Rstar(ilagged,:)*eehat(:,k)+Cstar(ilagged);
end
elseif k>d+1
opts_simul.curb_retrench = options_.occbin.smoother.curb_retrench;
opts_simul.waitbar = options_.occbin.smoother.waitbar;
opts_simul.maxit = options_.occbin.smoother.maxit;
opts_simul.periods = options_.occbin.smoother.periods;
opts_simul.check_ahead_periods = options_.occbin.smoother.check_ahead_periods;
opts_simul.full_output = options_.occbin.smoother.full_output;
opts_simul.piecewise_only = options_.occbin.smoother.piecewise_only;
opts_simul.SHOCKS = zeros(nk,M_.exo_nbr);
opts_simul.SHOCKS(1,:) = eehat(:,k);
tmp=zeros(M_.endo_nbr,1);
tmp(oo_.dr.restrict_var_list,1)=aahat(:,k-1);
opts_simul.endo_init = tmp(oo_.dr.inv_order_var,1);
opts_simul.init_regime = []; %regimes_(k);
opts_simul.waitbar=0;
options_.occbin.simul=opts_simul;
[~, out] = occbin.solver(M_,options_,oo_.dr,oo_.steady_state,oo_.exo_steady_state,oo_.exo_det_steady_state);
% regime in out should be identical to regimes_(k-2) moved one
% period ahead (so if regimestart was [1 5] it should be [1 4]
% in out
% end
bbb(oo_.dr.inv_order_var,k) = out.piecewise(1,:) - out.ys';
end
end
ahat0=ahat;
ahat=bbb;
if ~isempty(P)
PP=zeros(M_.endo_nbr,M_.endo_nbr,gend+1);
PP(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:)=P;
P=PP;
clear PP
end
if ~isempty(state_uncertainty)
mm=size(T,1);
sstate_uncertainty=zeros(M_.endo_nbr,M_.endo_nbr,gend);
sstate_uncertainty(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:)=state_uncertainty(1:mm,1:mm,:);
state_uncertainty=sstate_uncertainty;
clear sstate_uncertainty
end
if ~isempty(state_uncertainty0)
mm=size(T,1);
sstate_uncertainty=zeros(M_.endo_nbr,M_.endo_nbr);
sstate_uncertainty(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list)=state_uncertainty0(1:mm,1:mm);
state_uncertainty0=sstate_uncertainty;
clear sstate_uncertainty
end
aaa = zeros(nk,M_.endo_nbr,gend+nk);
aaa(:,oo_.dr.restrict_var_list,:)=aK;
for k=2:gend+1
opts_simul.curb_retrench = options_.occbin.smoother.curb_retrench;
opts_simul.waitbar = options_.occbin.smoother.waitbar;
opts_simul.maxit = options_.occbin.smoother.maxit;
opts_simul.periods = options_.occbin.smoother.periods;
opts_simul.check_ahead_periods = options_.occbin.smoother.check_ahead_periods;
opts_simul.full_output = options_.occbin.smoother.full_output;
opts_simul.piecewise_only = options_.occbin.smoother.piecewise_only;
opts_simul.SHOCKS = zeros(nk,M_.exo_nbr);
tmp=zeros(M_.endo_nbr,1);
tmp(oo_.dr.restrict_var_list,1)=ahat0(:,k-1);
opts_simul.endo_init = tmp(oo_.dr.inv_order_var,1);
opts_simul.init_regime = []; %regimes_(k);
opts_simul.waitbar=0;
options_.occbin.simul=opts_simul;
[~, out] = occbin.solver(M_,options_,oo_.dr,oo_.steady_state,oo_.exo_steady_state,oo_.exo_det_steady_state);
% regime in out should be identical to regimes_(k-2) moved one
% period ahead (so if regimestart was [1 5] it should be [1 4]
% in out
% end
for jnk=1:nk
aaa(jnk,oo_.dr.inv_order_var,k+jnk-1) = out.piecewise(jnk,:) - out.ys';
end
end
aK=aaa;
if ~isempty(PK)
PP = zeros(nk,M_.endo_nbr,M_.endo_nbr,gend+nk);
PP(:,oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:) = PK;
PK=PP;
clear PP
end
else
% reconstruct smoother
[A,B] = kalman_transition_matrix(oo_.dr,(1:M_.endo_nbr)',ic);
iT = pinv(T);
Tstar = A(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list),oo_.dr.restrict_var_list);
Rstar = B(~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list),:);
C = Tstar*iT;
D = Rstar-C*R;
static_var_list = ~ismember(1:M_.endo_nbr,oo_.dr.restrict_var_list);
ilagged = any(abs(C*T-Tstar)'>1.e-12);
static_var_list0 = static_var_list;
static_var_list0(static_var_list) = ilagged;
static_var_list(static_var_list) = ~ilagged;
% reconstruct smoothed variables
aaa=zeros(M_.endo_nbr,gend+1);
if ~isempty(alphahat0)
aaa(oo_.dr.restrict_var_list,1)=alphahat0;
end
aaa(oo_.dr.restrict_var_list,2:end)=alphahat;
for k=1:gend aaa(static_var_list,k+1) = C(~ilagged,:)*alphahat(:,k)+D(~ilagged,:)*etahat(:,k);
end
if any(ilagged)
for k=2:gend
aaa(static_var_list0,k+1) = Tstar(ilagged,:)*alphahat(:,k-1)+Rstar(ilagged,:)*etahat(:,k);
end
aaa(static_var_list0,2) = Tstar(ilagged,:)*alphahat0+Rstar(ilagged,:)*etahat(:,1);
end
alphahat0=aaa(:,1);
alphahat=aaa(:,2:end);
% reconstruct updated variables
aaa=zeros(M_.endo_nbr,gend);
aaa(oo_.dr.restrict_var_list,:)=ahat;
for k=1:gend
aaa(static_var_list,k) = C(~ilagged,:)*ahat(:,k)+D(~ilagged,:)*eehat(:,k);
end
if any(ilagged)
% bbb=zeros(M_.endo_nbr,gend);
% bbb(oo_.dr.restrict_var_list,:)=aahat;
if ~isempty(aalphahat0)
aaa(static_var_list0,d+1) = Tstar(ilagged,:)*aalphahat0+Rstar(ilagged,:)*eehat(:,d+1);
end
for k=d+2:gend
aaa(static_var_list0,k) = Tstar(ilagged,:)*aahat(:,k-1)+Rstar(ilagged,:)*eehat(:,k);
end
end
ahat1=aaa;
% reconstruct aK
aaa = zeros(nk,M_.endo_nbr,gend+nk);
aaa(:,oo_.dr.restrict_var_list,:)=aK;
for k=1:gend
for jnk=1:nk
aaa(jnk,static_var_list,k+jnk) = C(~ilagged,:)*dynare_squeeze(aK(jnk,:,k+jnk));
end
end
if any(ilagged)
for k=1:gend
aaa(1,static_var_list0,k+1) = Tstar(ilagged,:)*ahat(:,k);
for jnk=2:nk
aaa(jnk,static_var_list0,k+jnk) = Tstar(ilagged,:)*dynare_squeeze(aK(jnk-1,:,k+jnk-1));
end
end
end
aK=aaa;
ahat=ahat1;
% reconstruct P
if ~isempty(P)
PP=zeros(M_.endo_nbr,M_.endo_nbr,gend+1);
PP(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:)=P;
if ~options_.heteroskedastic_filter
DQD=D(~ilagged,:)*Q*transpose(D(~ilagged,:))+C(~ilagged,:)*R*Q*transpose(D(~ilagged,:))+D(~ilagged,:)*Q*transpose(C(~ilagged,:)*R);
DQR=D(~ilagged,:)*Q*transpose(R);
end
for k=1:gend+1
if options_.heteroskedastic_filter
DQD=D(~ilagged,:)*Q(:,:,k)*transpose(D(~ilagged,:))+C(~ilagged,:)*R*Q(:,:,k)*transpose(D(~ilagged,:))+D(~ilagged,:)*Q(:,:,k)*transpose(C(~ilagged,:)*R);
DQR=D(~ilagged,:)*Q(:,:,k)*transpose(R);
end
PP(static_var_list,static_var_list,k)=C(~ilagged,:)*P(:,:,k)*C(~ilagged,:)'+DQD;
PP(static_var_list,oo_.dr.restrict_var_list,k)=C(~ilagged,:)*P(:,:,k)+DQR;
PP(oo_.dr.restrict_var_list,static_var_list,k)=transpose(PP(static_var_list,oo_.dr.restrict_var_list,k));
end
P=PP;
clear PP
end
% reconstruct state_uncertainty
if ~isempty(state_uncertainty) mm=size(T,1);
ss=length(find(static_var_list));
sstate_uncertainty=zeros(M_.endo_nbr,M_.endo_nbr,gend);
sstate_uncertainty(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:)=state_uncertainty(1:mm,1:mm,:);
for k=1:gend
sstate_uncertainty(static_var_list,static_var_list,k)=[C(~ilagged,:) D(~ilagged,:)]*state_uncertainty(:,:,k)*[C(~ilagged,:) D(~ilagged,:)]';
tmp = [C(~ilagged,:) D(~ilagged,:)]*state_uncertainty(:,:,k);
sstate_uncertainty(static_var_list,oo_.dr.restrict_var_list,k)=tmp(1:ss,1:mm);
sstate_uncertainty(oo_.dr.restrict_var_list,static_var_list,k)=transpose(sstate_uncertainty(static_var_list,oo_.dr.restrict_var_list,k));
end
state_uncertainty=sstate_uncertainty;
clear sstate_uncertainty
end
if ~isempty(state_uncertainty0)
mm=size(T,1);
ss=length(find(static_var_list));
sstate_uncertainty=zeros(M_.endo_nbr,M_.endo_nbr);
sstate_uncertainty(oo_.dr.restrict_var_list,oo_.dr.restrict_var_list)=state_uncertainty0(1:mm,1:mm);
sstate_uncertainty(static_var_list,static_var_list)=[C(~ilagged,:) D(~ilagged,:)]*state_uncertainty0*[C(~ilagged,:) D(~ilagged,:)]';
tmp = [C(~ilagged,:) D(~ilagged,:)]*state_uncertainty0;
sstate_uncertainty(static_var_list,oo_.dr.restrict_var_list)=tmp(1:ss,1:mm);
sstate_uncertainty(oo_.dr.restrict_var_list,static_var_list)=transpose(sstate_uncertainty(static_var_list,oo_.dr.restrict_var_list));
state_uncertainty0=sstate_uncertainty;
clear sstate_uncertainty
end
% reconstruct PK
if ~isempty(PK)
PP = zeros(nk,M_.endo_nbr,M_.endo_nbr,gend+nk);
PP(:,oo_.dr.restrict_var_list,oo_.dr.restrict_var_list,:) = PK;
if ~options_.heteroskedastic_filter
DQD=D(~ilagged,:)*Q*transpose(D(~ilagged,:))+C(~ilagged,:)*R*Q*transpose(D(~ilagged,:))+D(~ilagged,:)*Q*transpose(C(~ilagged,:)*R);
DQR=D(~ilagged,:)*Q*transpose(R);
for f=1:nk
for k=1:gend
PP(f,static_var_list,static_var_list,k+f)=C(~ilagged,:)*squeeze(PK(f,:,:,k+f))*C(~ilagged,:)'+DQD;
PP(f,static_var_list,oo_.dr.restrict_var_list,k+f)=C(~ilagged,:)*squeeze(PK(f,:,:,k+f))+DQR;
PP(f,oo_.dr.restrict_var_list,static_var_list,k+f)=transpose(squeeze(PP(f,static_var_list,oo_.dr.restrict_var_list,k+f)));
end
end
end
PK=PP;
clear PP
end
end
bayestopt_.mf = bayestopt_.smoother_var_list(bayestopt_.smoother_mf);
end
function a=set_Kalman_smoother_starting_values(a,M_,oo_,options_)
% function a=set_Kalman_smoother_starting_values(a,M_,oo_,options_)
% Sets initial states guess for Kalman filter/smoother based on M_.filter_initial_state
%
% INPUTS
% o a [double] (p*1) vector of states
% o M_ [structure] decribing the model
% o oo_ [structure] storing the results
% o options_ [structure] describing the options
%
% OUTPUTS
% o a [double] (p*1) vector of set initial states
if isfield(M_,'filter_initial_state') && ~isempty(M_.filter_initial_state)
state_indices=oo_.dr.order_var(oo_.dr.restrict_columns);
for ii=1:size(state_indices,1)
if ~isempty(M_.filter_initial_state{state_indices(ii),1})
if options_.loglinear && ~options_.logged_steady_state
a(oo_.dr.restrict_columns(ii)) = log(eval(M_.filter_initial_state{state_indices(ii),2})) - log(oo_.dr.ys(state_indices(ii)));
elseif ~options_.loglinear && ~options_.logged_steady_state
a(oo_.dr.restrict_columns(ii)) = eval(M_.filter_initial_state{state_indices(ii),2}) - oo_.dr.ys(state_indices(ii)); else
error(['The steady state is logged. This should not happen. Please contact the developers'])
end
end
end
end