Add unit test for smoother only on nonstationary model

tests/Makefile.am

@@ -193,6 +193,7 @@ MODFILES = \
 	kalman_filter_smoother/fs2000_2.mod \
 	kalman_filter_smoother/fs2000a.mod \
 	kalman_filter_smoother/fs2000_smoother_only.mod \
+	kalman_filter_smoother/fs2000_smoother_only_ns.mod \
 	kalman_filter_smoother/check_variable_dimensions/fs2000.mod \
 	kalman_filter_smoother/check_variable_dimensions/fs2000_ML.mod \
 	kalman/likelihood_from_dynare/fs2000_corr_ME.mod \

tests/kalman_filter_smoother/fs2000_smoother_only_ns.mod

+/*
+ * This file replicates the estimation of the cash in advance model described
+ * Frank Schorfheide (2000): "Loss function-based evaluation of DSGE models",
+ * Journal of Applied Econometrics, 15(6), 645-670.
+ *
+ * The data are in file "fsdat_simul.m", and have been artificially generated.
+ * They are therefore different from the original dataset used by Schorfheide.
+ *
+ * The equations are taken from J. Nason and T. Cogley (1994): "Testing the
+ * implications of long-run neutrality for monetary business cycle models",
+ * Journal of Applied Econometrics, 9, S37-S70.
+ * Note that there is an initial minus sign missing in equation (A1), p. S63.
+ *
+ * This implementation was written by Michel Juillard. Please note that the
+ * following copyright notice only applies to this Dynare implementation of the
+ * model.
+ */
+
+/*
+ * Copyright (C) 2004-2010 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 m P c e W R k d n l gy_obs gp_obs Y_obs P_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;
+Y_obs/Y_obs(-1) = gy_obs;
+P_obs/P_obs(-1) = gp_obs;
+end;
+
+steady_state_model;
+  dA = exp(gam);
+  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;
+  ist  = y-c;
+  q  = 1 - d;
+
+  e = 1;
+  
+  gp_obs = m/dA;
+  gy_obs = dA;
+  Y_obs = gy_obs;
+  P_obs = gp_obs;
+end;
+
+shocks;
+var e_a; stderr 0.014;
+var e_m; stderr 0.005;
+end;
+
+varobs P_obs Y_obs;
+
+observation_trends;
+P_obs (log(mst)-gam);
+Y_obs (gam);
+end;
+
+estimation(order=1, datafile=fsdat_simul, mode_compute=0,nobs=192, loglinear,diffuse_filter, smoother) m P c e W R k d n l gy_obs gp_obs y dA;
+estimation(order=1, datafile=fsdat_simul, mode_compute=0,nobs=192, loglinear,diffuse_filter, smoother,kalman_algo=3) m P c e W R k d n l gy_obs gp_obs y dA;
+estimation(order=1, datafile=fsdat_simul, mode_compute=0,nobs=192, loglinear,diffuse_filter, smoother,kalman_algo=4) m P c e W R k d n l gy_obs gp_obs y dA;
+
+/*
+ * The following lines were used to generate the data file. If you want to
+ * generate another random data file, comment the "estimation" line and uncomment
+ * the following lines.
+ */
+
+//stoch_simul(periods=200, order=1);
+//datatomfile('fsdat_simul', char('gy_obs', 'gp_obs'));