clc
clear all
close all

%{
vlastnosti odhadu OLS pro jednorovnicovy model s nesplnenymi predpoklady
    y1 = a1 + a2*x1 + a3*x2 + e
-konzistence
-nestrannost
-asymptoticka nestrannost
%}

a1 = 10.0; a2 = 5.0; a3 = 15.0;


disp('KONZISTENCE');
maxnobs = 1000;
OLS = zeros(3,maxnobs-10);
disp('probihaji regrese pro konzistenci!');
tic;
for i=10:maxnobs
    x1 = (randn(i,1)*10+6); x2 = randn(i,1)*4+3;
    iota = ones(i,1);
    y1 = zeros(i,1); evec = randn(i,1);%.*x1; %evec = 1+x1+x2+randn(i,1);
        %for k=2:length(evec) %autokorelace
        %    evec(k)=0.8*evec(k-1)+randn;
        %end
        for j = 1:i
            y1(j,1) = iota(j,1)*a1 + x1(j,1)*a2 +  x2(j,1)*a3 +evec(j,1);
        end;
    result = ols(y1,[iota x1 x2]);
    OLS(:,i-9) = result.beta;
end;

fprintf('\n Celkovy cas vypoctu pro konzistenci %6.2f sekund \n \n',toc);

figure
    subplot(1,3,1)
        plot(OLS(1,:));
        title('a1');
    subplot(1,3,2)
        plot(OLS(2,:));
        title('a2');
    subplot(1,3,3)
        plot(OLS(3,:));
        title('a3');

disp('NESTRANNOST');
nobs = 100;
niter = 1000;
disp('probihaji regrese pro nestrannost!');
tic;
OLS = zeros(3,niter);
evec = zeros(nobs,1);
x1 = randn(nobs,1)*10+6; x2 = randn(nobs,1)*4+3;
iota = ones(nobs,1);
for iter = 1:niter;
        y1 = zeros(nobs,1); evec = randn(nobs,1);%.*x1; %evec =1+x1+x2+randn(nobs,1);
            %for k=2:length(evec) %autokorelace
            % evec(k)=0.8*evec(k-1)+randn;
            %end
        for j = 1:nobs
            y1(j,1) = iota(j,1)*a1 + x1(j,1)*a2 + x2(j,1)*a3 +evec(j,1);
        end;
        result = ols(y1,[iota x1 x2]);
        OLS(:,iter) = result.beta;
end;
OLSm = mean(OLS,2);

fprintf('\n Celkovy cas vypoctu pro nestrannost %6.2f sekund \n \n',toc);
fprintf(['\n Delka vzorku je ',num2str(nobs),'\n']);
fprintf(['OLS vysledky prvni rovnice pres ', num2str(niter),' iteraci \n']);
in.rnames = strvcat('Koeficient','a1','a2','a3');
in.cnames = strvcat('mean');
mprint([OLSm],in);

%{
disp('ASYMPTOTICKA NESTRANNOST')
niter = 50;
maxnobs = 200;
OLS = zeros(3,niter);
OLSm = zeros(3,maxnobs-10);

disp('probihaji regrese pro asymptotickou nestrannost!');
tic;
for i=10:maxnobs
    x1 = randn(i,1); x2 = randn(i,1);
    iota = ones(i,1);
    for iter = 1:niter;
        y1 = zeros(i,1); evec = randn(i,1);
        for j = 1:i
            y1(j,1) = iota(j,1)*a1 + x1(j,1)*a2 + x2(j,1)*a3 +evec(j,1);
        end;
        result = ols(y1,[iota x1 x2]);
        OLS(:,iter) = result.beta;
    end;
    OLSm(:,i-9) = mean(OLS,2);
end;

fprintf('\n Celkovy cas vypoctu pro asymptotickou nestrannost %6.2f sekund \n \n',toc);

figure
    subplot(1,3,1)
        plot(OLSm(1,:));
        title('mean a1');
    subplot(1,3,2)
        plot(OLSm(2,:));
        title('mean a2');
    subplot(1,3,3)
        plot(OLSm(3,:));
        title('mean a3');
%}