forecasting - Matlab Kalman Filter Code - Forecast h-steps ahead? -

i have following code forecast variable zhi. far can see result ezhivec(i) given me the t+1 observation.

but want compute h-steps ahead forecasts , absolutely don't know how...

clear all;  %  state space reprsentation forcasted kalman filter %   zhi(t+1) = f*zhi(t) + v(t+1)   --> unbobserved varaibles %   v~n(0,q) %   y(t) = a'*x(t) + h'*zhi(t) + w(t) %   w~n(0,r)  global y; global x; global hvec; %%----    enter  input parameters load hon.txt %filename stock prices load dji.txt %filename index prices n=100; %no. of points consider offset=1; %use 1 daily return or 30 monthly return %-------------------------------   datapts=1:offset:(n+1)*offset; dji=dji(datapts); hon=hon(datapts);  %hvec=(dji(1:n)-dji(2:n+1))./dji(2:n+1); %index returns process %y=(hon(1:n)-hon(2:n+1))./hon(2:n+1); %index returns process  hvec=log(dji(1:n)./dji(2:n+1)); %index returns process y=log(hon(1:n)./hon(2:n+1)); %stock returns process  hvec=flipud(hvec); y=flipud(y);   x=ones(n,1);     param=zeros(5,1); f=0.5; f=-log(1/f-1); param(1)=f; param(2)=0.2; param(3)=1; param(4)=0.2; param(5)=0.5;  resultparam=fminsearch(mylikelihoodfn,param)   f=resultparam(1) f=1/(1+exp(-f)) q=resultparam(2)^2 a=resultparam(3) r=resultparam(4)^2 betai=resultparam(5)  n=size(y,1); p=q; ezhi=0.01; ezhivec=zeros(n,1); ezhivec(1)=ezhi;  i=2:n   yt=y(i);   xt=x(i);   h=hvec(i);   ezhi = f*ezhi + f*p*h*inv(h'*p*h+r)*(yt-a'*xt-h'*betai-h'*ezhi);   p = f*p*f' - f*p*h*inv(h'*p*h+r)*h'*p*f' + q;   ezhivec(i)=ezhi; end ezhivec=ezhivec+betai; test=[ezhivec hvec y]; tmp=1:n; subplot(3,1,1); plot(tmp,y,'-'); subplot(3,1,2); plot(tmp,hvec,'-'); subplot(3,1,3); plot(tmp,ezhivec,'-');  %plot(tmp,ezhivec,'-',tmp,hvec,'-',tmp,y,'-'); %plot(tmp,zhi,'-',tmp,ezhivec,'-');   %% ------------------ %test=[zhi y]  function ret=mylikelihoodfn(p)   global y;   global x;   global hvec;   f=p(1);   f=1/(1+exp(-f));   q=p(2)^2;   a=p(3);   r=p(4)^2;   betai=p(5);   n=size(y,1);   p=q;   ezhi=0;   ezhivec=zeros(n,1);   ezhivec(1)=ezhi;   tmpsum=0;   tmp1=-(n/2)*log(2*pi);   i=2:n     yt=y(i);     xt=x(i);     h=hvec(i);     ezhi = f*ezhi + f*p*h*inv(h'*p*h+r)*(yt-a'*xt-h'*betai-h'*ezhi);     p = f*p*f' - f*p*h*inv(h'*p*h+r)*h'*p*f' + q;     ezhivec(i)=ezhi;     tmpmat = h'*p*h + r;     tmp2 = -0.5*log(det(tmpmat));     tmpmat2 = yt - a'*xt - h'*betai - h'*ezhi;     tmp3=-0.5*tmpmat2'*inv(tmpmat)*tmpmat2;     tmpsum=tmp1+tmp2+tmp3;   end   ret=-tmpsum;    end