clear;
addpath('functions');
T=500;
B1=0.25;
B2=0.9;
MU1=3;
MU2=-1;
S1=1;
S2=2;
P0=[0.98 0.02;0.02 0.98];
P=matf(P0,2,1);
strue=zeros(T,4);
strue(1,1)=1;
strue=simS(strue,P);
e=randn(T,1);
Y=zeros(T,1);
X=zeros(T,1);
for i=2:T;
X(i,:)=Y(i-1,:);
if strue(i,1)==1
Y(i)=(X(i,:)-MU1)*B1+MU1+e(i)*sqrt(S1);
elseif strue(i,2)==1
Y(i)=(X(i,:)-MU1)*B1+MU2+e(i)*sqrt(S2);
elseif strue(i,3)==1
Y(i)=(X(i,:)-MU2)*B1+MU1+e(i)*sqrt(S1);
else
Y(i)=(X(i,:)-MU2)*B1+MU2+e(i)*sqrt(S2);
end
end
y=Y;
x=X;
phi=0.5;
mu1=1;
mu2=0.1;
sig1=1;
sig2=1;
p=0.95;
q=0.95;
pmat0=[p 1-q;1-p q];
pmat=matf(pmat0,2,1);
ncrit=10;
B0=zeros(1,1);
Sigma0=eye(1);
M0=zeros(2,1);
Sigma0M=eye(2)*10;
d0=0.1;
v0=1;
u00=25;
u01=5;
u11=25;
u10=5;
out1=[];
out2=[];
out3=[];
out4=[];
REPS=10000;
BURN=5000;
igibbs=1;
count=1;
while count<REPS-BURN
A = [(eye(4)-pmat);ones(1,4)];
EN=[0;0;0;0;1];
ett11= pinv(A'*A)*A'*EN;
isig1=1/sig1;
isig2=1/sig2;
isig3=1/sig1;
isig4=1/sig2;
lik=0;
filter=zeros(T,4);
for j=1:T
em1=(y(j)-mu1)-(x(j,:)-mu1)*phi;
em2=(y(j)-mu2)-(x(j,:)-mu1)*phi;
em3=(y(j)-mu1)-(x(j,:)-mu2)*phi;
em4=(y(j)-mu2)-(x(j,:)-mu2)*phi;
neta1=(1/sqrt(sig1))*exp(-0.5*(em1*isig1*em1'));
neta2=(1/sqrt(sig2))*exp(-0.5*(em2*isig2*em2'));
neta3=(1/sqrt(sig1))*exp(-0.5*(em3*isig3*em3'));
neta4=(1/sqrt(sig2))*exp(-0.5*(em4*isig4*em4'));
ett10=pmat*ett11;
ett11=ett10.*[neta1;neta2;neta3;neta4];
fit=sum(ett11);
ett11=(ett11)/fit;
filter(j,1:4)=ett11';
lik=lik+log(fit);
end
check=-1;
while check<0
S=zeros(T,1);
p1=filter(T,1);
p2=filter(T,2);
p3=filter(T,3);
p4=filter(T,4);
p=p1/(p1+p2+p3+p4);
u=rand(1,1);
temp=(u>=p);
if temp==0
S(T)=1;
else
p=p2/(p2+p3+p4);
u=rand(1,1);
temp=(u>=p);
if temp==0
S(T)=2;
else
p=p3/(p3+p4);
u=rand(1,1);
temp=(u>=p);
if (temp==0)
S(T)=3;
else
S(T)=4;
end
end
end
for t=T-1:-1:1
if S(t+1)==1
p1=pmat(1,1)*filter(t,1);
p2=pmat(1,2)*filter(t,2);
p3=pmat(1,3)*filter(t,3);
p4=pmat(1,4)*filter(t,4);
elseif S(t+1)==2
p1=pmat(2,1)*filter(t,1);
p2=pmat(2,2)*filter(t,2);
p3=pmat(2,3)*filter(t,3);
p4=pmat(2,4)*filter(t,4);
elseif S(t+1)==3
p1=pmat(3,1)*filter(t,1);
p2=pmat(3,2)*filter(t,2);
p3=pmat(3,3)*filter(t,3);
p4=pmat(3,4)*filter(t,4);
elseif S(t+1)==4
p1=pmat(4,1)*filter(t,1);
p2=pmat(4,2)*filter(t,2);
p3=pmat(4,3)*filter(t,3);
p4=pmat(4,4)*filter(t,4);
end
p=p1/(p1+p2+p3+p4);
u=rand(1,1);
temp=(u>=p);
if temp==0
S(t)=1;
else
p=p2/(p2+p3+p4);
u=rand(1,1);
temp=(u>=p);
if temp==0
S(t)=2;
else
p=p3/(p3+p4);
u=rand(1,1);
temp=(u>=p);
if temp==0
S(t)=3;
else
S(t)=4;
end
end
end
end
if sum(((S==1)+(S==3))==1)>=ncrit && sum(((S==2)+(S==4))==1)>=ncrit
check=1;
end
end
Sstar=1-((S==1)+(S==3));
tranmat=switchg(Sstar+1,[1;2]);
N00=tranmat(1,1);
N01=tranmat(1,2);
N10=tranmat(2,1);
N11=tranmat(2,2);
p0=drchrnd([N00+u00;N01+u01]);
p=p0(1,1);
p0=drchrnd([N10+u10;N11+u11]);
q=p0(2,1);
pmat0=[p 1-q;1-p q];
pmat=matf(pmat0,2,1);
mut=(S==1).*mu1+(S==2).*mu2+(S==3).*mu1+(S==4).*mu2;
mutlag=(S==1).*mu1+(S==2).*mu1+(S==3).*mu2+(S==4).*mu2;
sigall=(S==1).*sig1+(S==2).*sig2+(S==3).*sig1+(S==4).*sig2;
ystar=(y-mut)./sqrt(sigall);
xstar=(x-mutlag)./sqrt(sigall);
V=inv(inv(Sigma0)+(xstar'*xstar));
M=V*(inv(Sigma0)*B0+xstar'*ystar);
phi=M+(randn(1,1)*chol(V))';
ystar=(y-x*phi)./sqrt(sigall);
xstar=([(Sstar==0).*(1-phi) (Sstar==1).*(1-phi)])./repmat(sqrt(sigall),1,2);
V=inv(inv(Sigma0M)+(xstar'*xstar));
M=V*(inv(Sigma0M)*M0+xstar'*ystar);
mu=M+(randn(1,2)*chol(V))';
mu1=mu(1);
mu2=mu(2);
resid=(y-mut)-(x-mutlag)*phi;
e1=resid(Sstar==0);
e2=resid(Sstar==1);
T1=v0+rows(e1);
D1=d0+e1'*e1;
z0=randn(T1,1);
z0z0=z0'*z0;
sig1=D1/z0z0;
T2=v0+rows(e2);
D2=d0+e2'*e2;
z0=randn(T2,1);
z0z0=z0'*z0;
sig2=D2/z0z0;
if igibbs>BURN
chck=mu1>mu2;
if chck
out1=[out1;([phi mu1 mu2])];
out2=[out2;([sig1 sig2 ])];
out3=[out3;Sstar'];
out4=[out4;[p q]];
count=count+1;
end
end
igibbs=igibbs+1
end
figure(1)
subplot(4,2,1);
hist(out1(:,1),50);
vline(B1)
title('AR Coefficient');
axis tight
subplot(4,2,3);
hist(out1(:,2),50);
vline(MU1)
title('mean regime 1');
axis tight
subplot(4,2,4);
hist(out1(:,3),50);
title('mean regime 2');
vline(MU2)
axis tight
subplot(4,2,5);
hist(out2(:,1),50);
vline(S1)
title('\sigma_{1}');
axis tight
subplot(4,2,6);
hist(out2(:,2),50);
vline(S2)
title('\sigma_{2}');
axis tight
subplot(4,2,7);
hist(out4(:,1),50);
title('P_{00}');
vline(P0(1,1))
axis tight
subplot(4,2,8);
hist(out4(:,2),50);
title('p_{11}');
vline(P0(2,2))
axis tight
figure(2)
temp=mean(out3,1);
plot(temp,'k');
hold on
plot(strue(:,2)+strue(:,4),'c')
title('Probability of Regime 2');
legend('Estimate','True')
axis tight