Added example with estimation of the PAC equation by NLS.

examples/9/clean

+#!/bin/sh
+
+rm -rf example
+rm  -f example*.json
+rm -f example*.m
+rm -f example*.mat
+rm -f example.log
+rm -f ssr_zpac.m

examples/9/example.mod

+// --+ options: json=compute, stochastic +--
+
+var x1 x2 x1bar x2bar z y;
+
+varexo ex1 ex2 ex1bar ex2bar ez ey;
+
+parameters
+       rho_1 rho_2
+       a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
+	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
+	   e_c_m c_z_1 c_z_2 gamma beta ;
+
+rho_1 = .9;
+rho_2 = -.2;
+
+a_x1_0 =  -.9;
+a_x1_1 =  .4;
+a_x1_2 =  .3;
+a_x1_x2_1 = .1;
+a_x1_x2_2 = .2;
+
+
+a_x2_0 =  -.9;
+a_x2_1 =   .2;
+a_x2_2 =  -.1;
+a_x2_x1_1 = -.1;
+a_x2_x1_2 = .2;
+
+beta  =  .2;
+e_c_m =  .5;
+c_z_1 =  .2;
+c_z_2 = -.1;
+
+gamma =  .7;
+
+var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
+
+pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
+
+model;
+
+[name='eq:y']
+y = rho_1*y(-1) + rho_2*y(-2) + ey;
+
+[name='eq:x1', data_type='nonstationary']
+diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     
+
+[name='eq:x2', data_type='nonstationary']
+diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     
+
+[name='eq:x1bar', data_type='nonstationary']
+x1bar = x1bar(-1) + ex1bar;
+
+[name='eq:x2bar', data_type='nonstationary']
+x2bar = x2bar(-1) + ex2bar;
+
+[name='zpac']
+diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
+
+end;
+
+shocks;
+    var ex1 = 1.0;
+    var ex2 = 1.0;
+    var ex1bar = 1.0;
+    var ex2bar = 1.0;
+    var ez = 1.0;
+    var ey = 0.1;
+end;
+
+// Build the companion matrix of the VAR model (toto).
+get_companion_matrix('toto', 'pacman');
+
+// Update the parameters of the PAC expectation model (h0 and h1 vectors).
+pac.update.expectation('pacman');
+
+// Set initial conditions to zero. Please use more sensible values if any...
+initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
+
+// Simulate the model for 500 periods
+TrueData = simul_backward_model(initialconditions, 500);
+
+//[pnames, enames, xnames, pid, eid, xid] = get_variables_and_parameters_in_equation('zpac', M_)
+
+// Define a structure describing the parameters to be estimated (with initial conditions). 
+eparams.e_c_m = .9;
+eparams.c_z_1 = .5;
+eparams.c_z_2 = .2;
+eparams.gamma = .1;
+
+// Define the dataset used for estimation
+edata = TrueData;
+edata.ez = dseries(NaN(TrueData.nobs, 1), 200Q1, 'ez');
+
+pac.estimate('zpac', eparams, edata, 2005Q1:2120Q1);
+
+disp(sprintf('Estimate of e_c_m: %f', M_.params(strmatch('e_c_m', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_1: %f', M_.params(strmatch('c_z_1', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of c_z_2: %f', M_.params(strmatch('c_z_2', M_.param_names, 'exact'))))
+disp(sprintf('Estimate of gamma: %f', M_.params(strmatch('gamma', M_.param_names, 'exact'))))