clear all
clc
w=xlsread('C:\final exam\rate of returns of USA house price index','sheet1','E2:G277');
rho_1_2=corr(w(:,1),w(:,2));
rho_1_3=corr(w(:,1),w(:,3));
rho_2_3=corr(w(:,2),w(:,3));
exenum=3; %執行模擬次數(加權平均分母)
betaTab=zeros(2,exenum);
%rho_1_2=0.5;
%rho_1_3=0.4;
%rho_2_3=0.3;
e=zeros(3,exenum);
% x1, x2 and x3 are indep.
e(1,:)=randn(1,exenum);
e(2,:)=randn(1,exenum);
e(3,:)=randn(1,exenum); % x1, x2 and x3 are indep.
Sigma=[1 rho_1_2 rho_1_3;rho_1_2 1 rho_2_3;rho_1_3 rho_2_3 1];
C=chol(Sigma);
V = C'*e ; % x1, x2 and x3 are dep.

for z=1:exenum; %模擬結果累加
    Y=w(:,1);
    Epslon=V(1,z);
    ini_guess=[0.001;0.001];
    bata(:,z)= lsqnonlin(@(bata) FE_1_1_fun(bata,Y,Epslon),ini_guess); %求估計係數
end
betaAve1=sum(bata,2)/exenum;
betaTab(:,1)=betaAve1;

for z=1:exenum; %模擬結果累加
    Y=w(:,2);
    Epslon=V(2,z);
    ini_guess=[0.001;0.001];
    bata(:,z)= lsqnonlin(@(bata) FE_1_1_fun(bata,Y,Epslon),ini_guess); %求估計係數
end
betaAve2=sum(bata,2)/exenum;
betaTab(:,2)=betaAve2;

for z=1:exenum; %模擬結果累加
    Y=w(:,3);
    Epslon=V(3,z);
    ini_guess=[0.001;0.001];
    bata(:,z)= lsqnonlin(@(bata) FE_1_1_fun(bata,Y,Epslon),ini_guess); %求估計係數
end
betaAve3=sum(bata,2)/exenum;
betaTab(:,3)=betaAve3;
betaTab