adding Ed Herbst fast implementation of the Kalman filter and test

cases with timing. Still needs preprocessor interface (option) and documentation.

matlab/kalman/likelihood/kalman_filter_fast.m

+function [LIK, LIKK, a, P] = kalman_filter_fast(Y,start,last,a,P,kalman_tol,riccati_tol,presample,T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods,analytic_derivation,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P)
+% [LIK, LIKK, a, P] =
+% kalman_filter_fast(Y,start,last,a,P,kalman_tol,riccati_tol,presample,T,Q,R,H,Z,mm,pp,rr,Zflag,diffuse_periods,analytic_derivation,DT,DYss,DOm,DH,DP,D2T,D2Yss,D2Om,D2H,D2P)
+% computes the likelihood of a stationnary state space model using Ed
+% Herbst fast implementation of the Kalman filter.
+
+%@info:
+%! @deftypefn {Function File} {[@var{LIK},@var{likk},@var{a},@var{P} ] =} kalman_filter_fast(@var{Y}, @var{start}, @var{last}, @var{a}, @var{P}, @var{kalman_tol}, @var{riccati_tol},@var{presample},@var{T},@var{Q},@var{R},@var{H},@var{Z},@var{mm},@var{pp},@var{rr},@var{Zflag},@var{diffuse_periods})
+%! @anchor{kalman_filter}
+%! @sp 1
+%! Computes the likelihood of a stationary state space model, given initial condition for the states (mean and variance).
+%! @sp 2
+%! @strong{Inputs}
+%! @sp 1
+%! @table @ @var
+%! @item Y
+%! Matrix (@var{pp}*T) of doubles, data.
+%! @item start
+%! Integer scalar, first period.
+%! @item last
+%! Integer scalar, last period (@var{last}-@var{first} has to be inferior to T).
+%! @item a
+%! Vector (@var{mm}*1) of doubles, initial mean of the state vector.
+%! @item P
+%! Matrix (@var{mm}*@var{mm}) of doubles, initial covariance matrix of the state vector.
+%! @item kalman_tol
+%! Double scalar, tolerance parameter (rcond, inversibility of the covariance matrix of the prediction errors).
+%! @item riccati_tol
+%! Double scalar, tolerance parameter (iteration over the Riccati equation).
+%! @item presample
+%! Integer scalar, presampling if strictly positive (number of initial iterations to be discarded when evaluating the likelihood).
+%! @item T
+%! Matrix (@var{mm}*@var{mm}) of doubles, transition matrix of the state equation.
+%! @item Q
+%! Matrix (@var{rr}*@var{rr}) of doubles, covariance matrix of the structural innovations (noise in the state equation).
+%! @item R
+%! Matrix (@var{mm}*@var{rr}) of doubles, second matrix of the state equation relating the structural innovations to the state variables.
+%! @item H
+%! Matrix (@var{pp}*@var{pp}) of doubles, covariance matrix of the measurement errors (if no measurement errors set H as a zero scalar).
+%! @item Z
+%! Matrix (@var{pp}*@var{mm}) of doubles or vector of integers, matrix relating the states to the observed variables or vector of indices (depending on the value of @var{Zflag}).
+%! @item mm
+%! Integer scalar, number of state variables.
+%! @item pp
+%! Integer scalar, number of observed variables.
+%! @item rr
+%! Integer scalar, number of structural innovations.
+%! @item Zflag
+%! Integer scalar, equal to 0 if Z is a vector of indices targeting the obseved variables in the state vector, equal to 1 if Z is a @var{pp}*@var{mm} matrix.
+%! @item diffuse_periods
+%! Integer scalar, number of diffuse filter periods in the initialization step.
+%! @end table
+%! @sp 2
+%! @strong{Outputs}
+%! @sp 1
+%! @table @ @var
+%! @item LIK
+%! Double scalar, value of (minus) the likelihood.
+%! @item likk
+%! Column vector of doubles, values of the density of each observation.
+%! @item a
+%! Vector (@var{mm}*1) of doubles, mean of the state vector at the end of the (sub)sample.
+%! @item P
+%! Matrix (@var{mm}*@var{mm}) of doubles, covariance of the state vector at the end of the (sub)sample.
+%! @end table
+%! @sp 2
+%! @strong{This function is called by:}
+%! @sp 1
+%! @ref{DsgeLikelihood}
+%! @sp 2
+%! @strong{This function calls:}
+%! @sp 1
+%! @ref{kalman_filter_ss}
+%! @end deftypefn
+%@eod:
+
+% Copyright (C) 2004-2013 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/>.
+
+
+% Set defaults.
+if nargin<17
+    Zflag = 0;
+end
+
+if nargin<18
+    diffuse_periods = 0;
+end
+
+if nargin<19
+    analytic_derivation = 0;
+end
+
+if isempty(Zflag)
+    Zflag = 0;
+end
+
+if isempty(diffuse_periods)
+    diffuse_periods = 0;
+end
+
+% Get sample size.
+smpl = last-start+1;
+
+% Initialize some variables.
+dF   = 1;
+QQ   = R*Q*transpose(R);   % Variance of R times the vector of structural innovations.
+t    = start;              % Initialization of the time index.
+likk = zeros(smpl,1);      % Initialization of the vector gathering the densities.
+LIK  = Inf;                % Default value of the log likelihood.
+oldK = Inf;
+notsteady   = 1;
+F_singular  = 1;
+asy_hess=0;
+
+DLIK=[];
+Hess=[];
+LIKK=[];
+
+if Zflag
+    K = T*P*Z';
+    F = Z*P*Z' + H;
+else
+    K = T*P(:,Z);
+    F = P(Z,Z) + H;
+end
+W = K;
+iF = inv(F);
+Kg = K*iF;
+M = -iF;
+
+while notsteady && t<=last
+    s = t-start+1;
+    if Zflag
+        v  = Y(:,t)-Z*a;
+    else
+        v  = Y(:,t)-a(Z);
+    end
+    if rcond(F) < kalman_tol
+        if ~all(abs(F(:))<kalman_tol)
+            return
+        else
+            a = T*a;
+            P = T*P*transpose(T)+QQ;
+        end
+    else
+        F_singular = 0;
+        dF      = det(F);
+        likk(s) = log(dF)+transpose(v)*iF*v;
+        a = T*a+Kg*v;
+        if Zflag
+            ZWM = Z*W*M;
+            ZWMWp = ZWM*W';
+            M = M + ZWM'*iF*ZWM;
+            F  = F + ZWMWp*Z';
+            iF      = inv(F);
+            K = K + T*ZWMWp';
+            Kg = K*iF;
+            W = (T - Kg*Z)*W;
+        else
+            ZWM = W(Z,:)*M;
+            ZWMWp = ZWM*W';
+            M = M + ZWM'*iF*ZWM;
+            F  = F + ZWMWp(:,Z);
+            iF      = inv(F);
+            K = K + T*ZWMWp';
+            Kg = K*iF;
+            W = T*W - Kg*W(Z,:);
+        end
+        %        notsteady = max(abs(K(:)-oldK))>riccati_tol;
+        oldK = K(:);
+    end
+    t = t+1;
+end
+
+if F_singular
+    error('The variance of the forecast error remains singular until the end of the sample')
+end
+
+% Add observation's densities constants and divide by two.
+likk(1:s) = .5*(likk(1:s) + pp*log(2*pi));
+if analytic_derivation,
+    DLIK = DLIK/2;
+    dlikk = dlikk/2;
+    if analytic_derivation==2 || asy_hess,
+        if asy_hess==0,
+        Hess = Hess + tril(Hess,-1)';
+        end
+        Hess = -Hess/2;
+    end
+end
+
+% Call steady state Kalman filter if needed.
+if t <= last
+    if analytic_derivation,
+        if analytic_derivation==2,
+            [tmp, tmp2] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag, ...
+                analytic_derivation,Da,DT,DYss,D2a,D2T,D2Yss);
+        else
+            [tmp, tmp2] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag, ...
+                analytic_derivation,Da,DT,DYss,asy_hess);
+        end
+        likk(s+1:end)=tmp2{1};
+        dlikk(s+1:end,:)=tmp2{2};
+        DLIK = DLIK + tmp{2};
+        if analytic_derivation==2 || asy_hess,
+            Hess = Hess + tmp{3};
+        end
+    else
+        [tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag);
+    end
+end
+
+% Compute minus the log-likelihood.
+if presample>diffuse_periods,
+    LIK = sum(likk(1+(presample-diffuse_periods):end));
+else
+    LIK = sum(likk);
+end
+
+if analytic_derivation,
+    if analytic_derivation==2 || asy_hess,
+        LIK={LIK, DLIK, Hess};
+    else
+        LIK={LIK, DLIK};
+    end
+    LIKK={likk, dlikk};
+else
+    LIKK=likk;
+end

tests/kalman_filter_fast/fs2000_a0.mod

+// See fs2000.mod in the examples/ directory for details on the model
+
+var m P c e W R k d n l gy_obs gp_obs y dA;
+varexo e_a e_m;
+
+parameters alp bet gam mst rho psi del;
+
+alp = 0.33;
+bet = 0.99;
+gam = 0.003;
+mst = 1.011;
+rho = 0.7;
+psi = 0.787;
+del = 0.02;
+
+model;
+dA = exp(gam+e_a);
+log(m) = (1-rho)*log(mst) + rho*log(m(-1))+e_m;
+-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
+W = l/n;
+-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
+R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
+1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
+c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
+P*c = m;
+m-1+d = l;
+e = exp(e_a);
+y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
+gy_obs = dA*y/y(-1);
+gp_obs = (P/P(-1))*m(-1)/dA;
+end;
+
+steady_state_model;
+  dA = exp(gam);
+  e = 1;
+  gst = 1/dA;
+  m = mst;
+
+  khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
+  xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
+  nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
+  n  = xist/(nust+xist);
+  P  = xist + nust;
+  k  = khst*n;
+  l  = psi*mst*n/( (1-psi)*(1-n) );
+  c  = mst/P;
+  d  = l - mst + 1;
+  y  = k^alp*n^(1-alp)*gst^alp;
+  R  = mst/bet;
+  W  = l/n;
+  
+  gp_obs = mst/dA;
+  gy_obs = dA;
+end;
+
+shocks;
+var e_a; stderr 0.014;
+var e_m; stderr 0.005;
+end;
+
+steady;
+
+check;
+
+estimated_params;
+alp, beta_pdf, 0.356, 0.02;
+bet, beta_pdf, 0.993, 0.002;
+gam, normal_pdf, 0.0085, 0.003;
+mst, normal_pdf, 1.0002, 0.007;
+rho, beta_pdf, 0.129, 0.223;
+psi, beta_pdf, 0.65, 0.05;
+del, beta_pdf, 0.01, 0.005;
+stderr e_a, inv_gamma_pdf, 0.035449, inf;
+stderr e_m, inv_gamma_pdf, 0.008862, inf;
+end;
+
+varobs gp_obs gy_obs;
+
+options_.solve_tolf = 1e-12;
+
+// this disable the switch to steady state filter
+options_.riccati_tol = 0;
+
+estimation(order=1,datafile=fsdat_simul,nobs=192,loglinear,mh_replic=2000,mh_nblocks=2,mh_jscale=0.8,plot_priors=0,mode_compute=0);

tests/kalman_filter_fast/fs2000_a1.mod

+// See fs2000.mod in the examples/ directory for details on the model
+
+var m P c e W R k d n l gy_obs gp_obs y dA;
+varexo e_a e_m;
+
+parameters alp bet gam mst rho psi del;
+
+alp = 0.33;
+bet = 0.99;
+gam = 0.003;
+mst = 1.011;
+rho = 0.7;
+psi = 0.787;
+del = 0.02;
+
+model;
+dA = exp(gam+e_a);
+log(m) = (1-rho)*log(mst) + rho*log(m(-1))+e_m;
+-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
+W = l/n;
+-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
+R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
+1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
+c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
+P*c = m;
+m-1+d = l;
+e = exp(e_a);
+y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
+gy_obs = dA*y/y(-1);
+gp_obs = (P/P(-1))*m(-1)/dA;
+end;
+
+steady_state_model;
+  dA = exp(gam);
+  e = 1;
+  gst = 1/dA;
+  m = mst;
+
+  khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
+  xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
+  nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
+  n  = xist/(nust+xist);
+  P  = xist + nust;
+  k  = khst*n;
+  l  = psi*mst*n/( (1-psi)*(1-n) );
+  c  = mst/P;
+  d  = l - mst + 1;
+  y  = k^alp*n^(1-alp)*gst^alp;
+  R  = mst/bet;
+  W  = l/n;
+  
+  gp_obs = mst/dA;
+  gy_obs = dA;
+end;
+
+shocks;
+var e_a; stderr 0.014;
+var e_m; stderr 0.005;
+end;
+
+steady;
+
+check;
+
+estimated_params;
+alp, beta_pdf, 0.356, 0.02;
+bet, beta_pdf, 0.993, 0.002;
+gam, normal_pdf, 0.0085, 0.003;
+mst, normal_pdf, 1.0002, 0.007;
+rho, beta_pdf, 0.129, 0.223;
+psi, beta_pdf, 0.65, 0.05;
+del, beta_pdf, 0.01, 0.005;
+stderr e_a, inv_gamma_pdf, 0.035449, inf;
+stderr e_m, inv_gamma_pdf, 0.008862, inf;
+end;
+
+varobs gp_obs gy_obs;
+
+options_.solve_tolf = 1e-12;
+
+options_.fast_kalman=1;
+estimation(order=1,datafile=fsdat_simul,nobs=192,loglinear,mh_replic=2000,mh_nblocks=2,mh_jscale=0.8,plot_priors=0,mode_compute=0);

tests/kalman_filter_fast/swk_0.mod

+// country_nbr must be passed on the command line: dynare swk_0 -Dcountry_nbr=3
+@#define countries = [1:country_nbr]
+
+var 
+@#for c in countries
+MC_@{c} E_@{c} EF_@{c} R_KF_@{c} QF_@{c} CF_@{c} IF_@{c} YF_@{c} LF_@{c} PIEF_@{c} WF_@{c} RF_@{c} R_K_@{c} Q_@{c} C_@{c} I_@{c} Y_@{c} L_@{c} PIE_@{c} W_@{c} R_@{c} EE_A_@{c} PIE_BAR_@{c} EE_B_@{c} EE_G_@{c} EE_L_@{c} EE_I_@{c} KF_@{c} K_@{c}
+@#endfor    
+;
+varexo 
+@#for c in countries
+E_A_@{c} E_B_@{c} E_G_@{c} E_L_@{c} E_I_@{c} ETA_R_@{c} E_PIE_BAR_@{c} ETA_Q_@{c} ETA_P_@{c} ETA_W_@{c}
+@#endfor
+;
+ 
+parameters xi_e lambda_w alpha czcap beta phi_i tau sig_c hab ccs cinvs phi_y gamma_w xi_w gamma_p xi_p sig_l r_dpi r_pie r_dy r_y rho rho_a rho_pb rho_b rho_g rho_l rho_i  ;
+alpha=.30;
+beta=.99;
+tau=0.025;
+ccs=0.6;
+cinvs=.22; 
+lambda_w = 0.5;
+phi_i= 6.771;
+sig_c=   1.353; 
+hab=    0.573;    
+xi_w=   0.737;
+sig_l=    2.400;
+xi_p=   0.908;
+xi_e= 0.599;
+gamma_w=    0.763;
+gamma_p=    0.469;
+czcap=    0.169;
+phi_y=    1.408;
+r_pie=     1.684;
+r_dpi=    0.14;
+rho=      0.961;
+r_y=      0.099;
+r_dy=     0.159;
+rho_a=    0.823;
+rho_b=    0.855;
+rho_g=    0.949;
+rho_l=   0.889;
+rho_i=   0.927;
+rho_pb=  0.924;
+
+
+model(linear); 
+@#for c in countries
+          CF_@{c} = (1/(1+hab))*(CF_@{c}(1)+hab*CF_@{c}(-1))-((1-hab)/((1+hab)*sig_c))*(RF_@{c}-PIEF_@{c}(1)-EE_B_@{c}) ;
+	      0 =  alpha*R_KF_@{c}+(1-alpha)*WF_@{c} -EE_A_@{c} ;
+          PIEF_@{c} = 0;
+	      IF_@{c} = (1/(1+beta))* ((  IF_@{c}(-1) + beta*(IF_@{c}(1)))+(1/phi_i)*QF_@{c})+0*ETA_Q_@{c}+EE_I_@{c} ;
+	      QF_@{c} = -(RF_@{c}-PIEF_@{c}(1))+(1-beta*(1-tau))*((1+czcap)/czcap)*R_KF_@{c}(1)+beta*(1-tau)*QF_@{c}(1) +0*EE_I_@{c} ;
+          KF_@{c} =  (1-tau)*KF_@{c}(-1)+tau*IF_@{c}(-1) ;
+	      YF_@{c} = (ccs*CF_@{c}+cinvs*IF_@{c})+EE_G_@{c}  ;
+	      YF_@{c} = 1*phi_y*( alpha*KF_@{c}+alpha*(1/czcap)*R_KF_@{c}+(1-alpha)*LF_@{c}+EE_A_@{c} ) ;
+	      WF_@{c} = (sig_c/(1-hab))*(CF_@{c}-hab*CF_@{c}(-1)) + sig_l*LF_@{c} - EE_L_@{c} ;
+	      LF_@{c} = R_KF_@{c}*((1+czcap)/czcap)-WF_@{c}+KF_@{c} ;
+          EF_@{c} = EF_@{c}(-1)+EF_@{c}(1)-EF_@{c}+(LF_@{c}-EF_@{c})*((1-xi_e)*(1-xi_e*beta)/(xi_e));
+	      C_@{c} = (hab/(1+hab))*C_@{c}(-1)+(1/(1+hab))*C_@{c}(1)-((1-hab)/((1+hab)*sig_c))*(R_@{c}-PIE_@{c}(1)-EE_B_@{c}) ;
+	      I_@{c} = (1/(1+beta))* ((  I_@{c}(-1) + beta*(I_@{c}(1)))+(1/phi_i)*Q_@{c} )+1*ETA_Q_@{c}+1*EE_I_@{c} ;
+	      Q_@{c} = -(R_@{c}-PIE_@{c}(1))+(1-beta*(1-tau))*((1+czcap)/czcap)*R_K_@{c}(1)+beta*(1-tau)*Q_@{c}(1) +EE_I_@{c}*0+0*ETA_Q_@{c} ;
+	      K_@{c} =  (1-tau)*K_@{c}(-1)+tau*I_@{c}(-1) ;
+	      Y_@{c} = (ccs*C_@{c}+cinvs*I_@{c})+ EE_G_@{c}   ;
+	      Y_@{c} = phi_y*( alpha*K_@{c}+alpha*(1/czcap)*R_K_@{c}+(1-alpha)*L_@{c} ) +phi_y*EE_A_@{c}  ;
+	      PIE_@{c} = (1/(1+beta*gamma_p))*((beta)*(PIE_@{c}(1)) +(gamma_p)*(PIE_@{c}(-1))+((1-xi_p)*(1-beta*xi_p)/(xi_p))*(MC_@{c}))  + ETA_P_@{c} ; 
+	      MC_@{c} = alpha*R_K_@{c}+(1-alpha)*W_@{c} -EE_A_@{c};
+	      W_@{c} =  (1/(1+beta))*(beta*W_@{c}(+1)+W_@{c}(-1))+(beta/(1+beta))*(PIE_@{c}(+1))-((1+beta*gamma_w)/(1+beta))*(PIE_@{c})+(gamma_w/(1+beta))*(PIE_@{c}(-1))-(1/(1+beta))*(((1-beta*xi_w)*(1-xi_w))/(((1+(((1+lambda_w)*sig_l)/(lambda_w))))*xi_w))*(W_@{c}-sig_l*L_@{c}-(sig_c/(1-hab))*(C_@{c}-hab*C_@{c}(-1))+EE_L_@{c})+ETA_W_@{c};
+	      L_@{c} = R_K_@{c}*((1+czcap)/czcap)-W_@{c}+K_@{c} ;
+	      R_@{c} = r_dpi*(PIE_@{c}-PIE_@{c}(-1))+(1-rho)*(r_pie*(PIE_@{c}(-1)-PIE_BAR_@{c})+r_y*(Y_@{c}-YF_@{c}))+r_dy*(Y_@{c}-YF_@{c}-(Y_@{c}(-1)-YF_@{c}(-1)))+rho*(R_@{c}(-1)-PIE_BAR_@{c})+PIE_BAR_@{c}+ETA_R_@{c};
+          E_@{c} = E_@{c}(-1)+E_@{c}(1)-E_@{c}+(L_@{c}-E_@{c})*((1-xi_e)*(1-xi_e*beta)/(xi_e));
+          EE_A_@{c} = (rho_a)*EE_A_@{c}(-1)  + E_A_@{c};
+	      PIE_BAR_@{c} = rho_pb*PIE_BAR_@{c}(-1)+ E_PIE_BAR_@{c} ;
+	      EE_B_@{c} = rho_b*EE_B_@{c}(-1) + E_B_@{c} ;
+	      EE_G_@{c} = rho_g*EE_G_@{c}(-1) + E_G_@{c} ;
+	      EE_L_@{c} = rho_l*EE_L_@{c}(-1) + E_L_@{c} ;
+	      EE_I_@{c} = rho_i*EE_I_@{c}(-1) + E_I_@{c} ;
+@#endfor
+end; 
+
+ 
+estimated_params;
+@#for c in countries
+stderr E_A_@{c},0.543,0.01,4,INV_GAMMA_PDF,0.4,2;
+stderr E_PIE_BAR_@{c},0.072,0.001,4,INV_GAMMA_PDF,0.02,10;
+stderr E_B_@{c},0.2694,0.01,4,INV_GAMMA_PDF,0.2,2;
+stderr E_G_@{c},0.3052,0.01,4,INV_GAMMA_PDF,0.3,2;
+stderr E_L_@{c},1.4575,0.1,6,INV_GAMMA_PDF,1,2;
+stderr E_I_@{c},0.1318,0.01,4,INV_GAMMA_PDF,0.1,2;
+stderr ETA_R_@{c},0.1363,0.01,4,INV_GAMMA_PDF,0.1,2;
+stderr ETA_Q_@{c},0.4842,0.01,4,INV_GAMMA_PDF,0.4,2;
+stderr ETA_P_@{c},0.1731,0.01,4,INV_GAMMA_PDF,0.15,2;
+stderr ETA_W_@{c},0.2462,0.1,4,INV_GAMMA_PDF,0.25,2;
+@#endfor
+rho_a,.9722,.1,.9999,BETA_PDF,0.85,0.1;
+rho_pb,.85,.1,.999,BETA_PDF,0.85,0.1;
+rho_b,.7647,.1,.99,BETA_PDF,0.85,0.1;
+rho_g,.9502,.1,.9999,BETA_PDF,0.85,0.1;
+rho_l,.9542,.1,.9999,BETA_PDF,0.85,0.1;
+rho_i,.6705,.1,.99,BETA_PDF,0.85,0.1;
+phi_i,5.2083,1,15,NORMAL_PDF,4,1.5;
+sig_c,0.9817,0.25,3,NORMAL_PDF,1,0.375;
+hab,0.5612,0.3,0.95,BETA_PDF,0.7,0.1;
+xi_w,0.7661,0.3,0.9,BETA_PDF,0.75,0.05;
+sig_l,1.7526,0.5,5,NORMAL_PDF,2,0.75;
+xi_p,0.8684,0.3,0.95,BETA_PDF,0.75,0.05;
+xi_e,0.5724,0.1,0.95,BETA_PDF,0.5,0.15;
+gamma_w,0.6202,0.1,0.99,BETA_PDF,0.75,0.15;
+gamma_p,0.6638,0.1,0.99,BETA_PDF,0.75,0.15;
+czcap,0.2516,0.01,2,NORMAL_PDF,0.2,0.075;
+phi_y,1.3011,1.001,2,NORMAL_PDF,1.45,0.125;
+r_pie,1.4616,1.2,2,NORMAL_PDF,1.7,0.1;
+r_dpi,0.1144,0.01,0.5,NORMAL_PDF,0.3,0.1;
+rho,0.8865,0.5,0.99,BETA_PDF,0.8,0.10;
+r_y,0.0571,0.01,0.2,NORMAL_PDF,0.125,0.05;
+r_dy,0.2228,0.05,0.5,NORMAL_PDF,0.0625,0.05;
+end;
+
+varobs 
+@#for c in countries
+Y_@{c} C_@{c} I_@{c} E_@{c} PIE_@{c} W_@{c} R_@{c}
+@#endfor
+;
+
+// set estimation globals
+estimation(datafile=pseudo_data,presample=40, first_obs=1, nobs=118, mh_replic=0, mode_compute=0,plot_priors=0);
+
+// get variables
+[dataset_,xparam1, M_, options_, oo_, estim_params_,bayestopt_] = dynare_estimation_init(var_list_, M_.fname, [], M_, options_, oo_, estim_params_, bayestopt_);
+
+// this disable the switch to steady state filter
+options_.riccati_tol = 0;
+
+// actual computation for timing
+tic;
+for i=1:100;
+	    fval = dsge_likelihood(xparam1,dataset_,options_,M_,estim_params_,bayestopt_,oo_,[]);
+end;
+
+toc;
+
+
+

tests/kalman_filter_fast/swk_1.mod

+// country_nbr must be passed on the command line: dynare swk_1 -Dcountry_nbr=3
+@#define countries = [1:country_nbr]
+
+var 
+@#for c in countries
+MC_@{c} E_@{c} EF_@{c} R_KF_@{c} QF_@{c} CF_@{c} IF_@{c} YF_@{c} LF_@{c} PIEF_@{c} WF_@{c} RF_@{c} R_K_@{c} Q_@{c} C_@{c} I_@{c} Y_@{c} L_@{c} PIE_@{c} W_@{c} R_@{c} EE_A_@{c} PIE_BAR_@{c} EE_B_@{c} EE_G_@{c} EE_L_@{c} EE_I_@{c} KF_@{c} K_@{c}
+@#endfor    
+;
+varexo 
+@#for c in countries
+E_A_@{c} E_B_@{c} E_G_@{c} E_L_@{c} E_I_@{c} ETA_R_@{c} E_PIE_BAR_@{c} ETA_Q_@{c} ETA_P_@{c} ETA_W_@{c}
+@#endfor
+;
+ 
+parameters xi_e lambda_w alpha czcap beta phi_i tau sig_c hab ccs cinvs phi_y gamma_w xi_w gamma_p xi_p sig_l r_dpi r_pie r_dy r_y rho rho_a rho_pb rho_b rho_g rho_l rho_i  ;
+alpha=.30;
+beta=.99;
+tau=0.025;
+ccs=0.6;
+cinvs=.22; 
+lambda_w = 0.5;
+phi_i= 6.771;
+sig_c=   1.353; 
+hab=    0.573;    
+xi_w=   0.737;
+sig_l=    2.400;
+xi_p=   0.908;
+xi_e= 0.599;
+gamma_w=    0.763;
+gamma_p=    0.469;
+czcap=    0.169;
+phi_y=    1.408;
+r_pie=     1.684;
+r_dpi=    0.14;
+rho=      0.961;
+r_y=      0.099;
+r_dy=     0.159;
+rho_a=    0.823;
+rho_b=    0.855;
+rho_g=    0.949;
+rho_l=   0.889;
+rho_i=   0.927;
+rho_pb=  0.924;
+
+
+model(linear); 
+@#for c in countries
+          CF_@{c} = (1/(1+hab))*(CF_@{c}(1)+hab*CF_@{c}(-1))-((1-hab)/((1+hab)*sig_c))*(RF_@{c}-PIEF_@{c}(1)-EE_B_@{c}) ;
+	      0 =  alpha*R_KF_@{c}+(1-alpha)*WF_@{c} -EE_A_@{c} ;
+          PIEF_@{c} = 0;
+	      IF_@{c} = (1/(1+beta))* ((  IF_@{c}(-1) + beta*(IF_@{c}(1)))+(1/phi_i)*QF_@{c})+0*ETA_Q_@{c}+EE_I_@{c} ;
+	      QF_@{c} = -(RF_@{c}-PIEF_@{c}(1))+(1-beta*(1-tau))*((1+czcap)/czcap)*R_KF_@{c}(1)+beta*(1-tau)*QF_@{c}(1) +0*EE_I_@{c} ;