var y delta_y x z;

varexo eps_x eps_z;

parameters rho sigma_z sigma_x;

// set parameter values
sigma_z=0.001;
sigma_x=0.01;
rho=0.9;

model;
z=rho*z(-1)+sigma_z*eps_z;
x=x(-1)+sigma_x*eps_x;
y=x+z;
delta_y=y-y(-1);
end;

steady_state_model;
x=0;
z=0;
y=0;
delta_y=0;
end;

//set shock variances
shocks;
    var eps_z=1;
    var eps_x=1;
end;

steady;
check;
varobs y delta_y; 
stoch_simul(order=1,irf=0);


estimated_params;
rho, 0.9;
sigma_z, 0.01;
sigma_x, 0.01;
end;
options_.diffuse_filter=1;
identification(lik_init=3,advanced=1);

The treatment of unit roots seems unsatisfactory. First, one needs to specify options_.diffuse_filter=1; because options_ used in dynare_estimation_init does not inherit the lik_init from the identification command (used only in options_ident) and also does not accept diffuse_filter. Second, some graphs are empty. My guess is because some unconditional moments are infinite.