Re: [Gretl-users] Estimation of a State Space Model with Exogenous Variables in the State Transition Equation

Em 21/08/2015, às 18:25, Riccardo (Jack) Lucchetti <r.lucchetti(a)univpm.it&gt; escreveu: > On Fri, 21 Aug 2015, Sven Schreiber wrote: > >> Am 21.08.2015 um 16:37 schrieb Fernando Fernandes Neto: >> Dear Sven, >> >> Thanks a lot for your attention. >> What you've commented makes a lot of sense to me. So actually, I would >> have a vector of Time Varying Coefficients (that would be my exogenous >> variables), and a vector of unitary constants, being added to the State? > > Forget my remark about the constant, that was probably off-track. What I > have in mind is more or less the following. Yeah, Sven's approach is very sensible and arguably the most natural. What follows is an example script in which I simulate and estimate a model like this: y_t = alpha_t + epsilon_t alpha_t = x_t + 0.5*alpha_{t-1} + u_t which is more or less like the example Sven suggested, with y_t and x_t are observable series, epsilon_t and u_t are wn processes, and alpha_t is the latent state variable. I guess you can adapt it to your needs relatively easily. <hansl> set echo off set messages off /* generate some data */ nulldata 256 set seed 21082015 # make things replicable setobs 1 1 --special-time-series series exo = 5 exo = 1 + 0.8 * exo(-1) + normal() # this could be anything, really series alpha = 10 series u = 0.5*normal() series e = 0.2*normal() alpha = exo + 0.5*alpha(-1) + u series y = alpha + e /* set up the state space model */ function void TV_statemat(matrix *F, matrix x) F[1,2] = x[$kalman_t] end function matrix mexo = {exo} scalar se = 0.5 scalar su = 0.7 matrix H = {1;0} matrix F = {1, 1; 0, 1} matrix Omega = {1,0;0,0} matrix a0 = {0; 1} matrix P0 = {1.0e12, 0; 0, 0} kalman obsy y obsymat H obsvar su statemat F ; TV_statemat(&F, mexo) statevar Omega inistate a0 inivar P0 end kalman /* now estimate */ matrix param = {0.5, 1, 1} matrix ahat series LL = 0 mle LL = err ? NA: $kalman_lnl su = param[2]^2 Omega[1,1] = param[3]^2 F[1,1] = param[1] err = kfilter() params param end mle -vh ahat = ksmooth() series latent_est = ahat[,1] print alpha latent_est -o </hansl> ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti ------------------------------------------------------- _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users