echo on
format compact
% DEMONSTRACE ODHADU PARAMETRU SIMULOVANEHO PROCESU AR(2)
%========================================================
close all
% GENEROVANI PROCESU
%-----------------------------------------------------------------------------
p=2;
n=1000; sigma2=2.25; sigma=sqrt(sigma2);
[x,phir,thetar]=armagen([0.5,0.2],[],n+10,sigma);
xx=x(n-p+1:n+10);   % Poledni dve + 10 budoucich pozorovanych hodnot
x=x(1:n)  ;         % Dosud pozorovane hodnoty
% ODHAD AUTOKOVARIANCNI FUNKCE
[xro,xroE,mi,miE,xacf]=acf(x,figure);
pause;
%-----------------------------------------------------------------------------
% ODHAD PARCIALNI AUTOKOVARIANCNI FUNKCE A PARAMETRU PROCESU
[xpacf,phi]=pacf(xacf,n,figure);
more on
phi.'         % ODHAD PARAMETRU
more off
pause;
%-----------------------------------------------------------------------------
% ZAVERECNY ODHAD S ODHADNUTYM RADEM p=2
[xpacf,phi,phiE,v]=pacf(xacf(1:p+1),n);
[phi,phiE].'  % ZAVERECNY ODHAD PARAMETRU a jejich konfidencni polosirky
v             % ZAVERECNY ODHAD ROZPTYLU sigma2
pause;
%-----------------------------------------------------------------------------%-----------------------------------------------------------------------------
% VYHLAZENA PREDIKCE
xs = [x(n-p+1:n);armagen([0.5,0.2],[],10,0,x(n-p+1:n))]; % IDEALNI VYHLAZENI
xse= [x(n-p+1:n);armagen( phi(1:p),[],10,0,x(n-p+1:n))]; % ODHADNUTE VYHLAZENI
t=(n-p+1:n+10).';
figure;plot(t,xs,'w',t,xse,'y--')
title('Vyhlazena predikce');
pause;
%-----------------------------------------------------------------------------% PREDIKCE POMOCI ODHADU
% ODHAD PREDIKCE VCETNE SUMU
xxe=[x(n-p+1:n);armagen(phi(1:2),[],10,sqrt(v),x)];
figure;plot(t,xx,'w',t,xxe,'y--')
title('Odhad predikce vcetne sumu c.1');
pause;
%-----------------------------------------------------------------------------
% JESTE JEDNOU SE ZNOVU GENEROVANYMI BUDOUCIMI HODNOTAMI
xx = [x(n-p+1:n);armagen([0.5,0.2],[],10,sigma  ,x)];
xxe= [x(n-p+1:n);armagen(phi(1:2) ,[],10,sqrt(v),x)];
figure;plot(t,xx,'w',t,xxe,'y--')
title('Odhad predikce vcetne sumu c.2');
pause;
% OPAKUJTE NEKOLIKRAT
echo off