clear;
addpath('functions');
T=500;
B1=0.2;
B2=0.9;
C1=1;
C2=-1;
S1=10;
S2=1;
P=[0.95 0.05;0.05 0.95];
Q=[0.97 0;0.03 1];
strue=zeros(T,2);
strue(1,1)=1;
strue=simS(strue,P);
vtrue=zeros(T,2);
vtrue(1,1)=1;
check=-1;
while check<0
vtrue=simS(vtrue,Q);
if sum(vtrue(:,1))>20
check=1;
end
end
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
if vtrue(i,1)==1
Y(i)=[X(i,:) 1]*[B1 C1]'+e(i)*sqrt(S1);
elseif vtrue(i,2)==1
Y(i)=[X(i,:) 1]*[B1 C1]'+e(i)*sqrt(S2);
end
elseif strue(i,2)==1
if vtrue(i,1)==1
Y(i)=[X(i,:) 1]*[B2 C2]'+e(i)*sqrt(S1);
elseif vtrue(i,2)==1
Y(i)=[X(i,:) 1]*[B2 C2]'+e(i)*sqrt(S2);
end
end
end
y=Y;
x=[X ones(T,1)];
phi1=[0.5;1];
phi2=[0.8;-1];
sig1=3;
sig2=1;
p=0.95;
q=0.95;
px=0.98;
pmat=[p 1-q;1-p q];
qmat=[px 0; 1-px 1];
VV=zeros(T,1);
ncrit=5;
B0=zeros(2,1);
Sigma0=eye(2);
d0=0.1;
v0=1;
u00=25;
u01=5;
u11=25;
u10=5;
v00=25;
v01=5;
out1=[];
out2=[];
out3=[];
out4=[];
out5=[];
REPS=10000;
BURN=5000;
igibbs=1;
count=1;
while count<REPS-BURN
A = [(eye(2)-pmat);ones(1,2)];
EN=[0;0;1];
ett11= pinv(A'*A)*A'*EN;
lik=0;
filter=zeros(T,2);
for j=1:T
if VV(j)==0
iS1=1/sig1;
iS2=1/sig1;
dsig1=sqrt(sig1);
dsig2=sqrt(sig1);
else
iS1=1/sig2;
iS2=1/sig2;
dsig1=sqrt(sig2);
dsig2=sqrt(sig2);
end
em1=y(j)-x(j,:)*phi1;
em2=y(j)-x(j,:)*phi2;
neta1=(1/dsig1)*exp(-0.5*(em1*iS1*em1'));
neta2=(1/dsig2)*exp(-0.5*(em2*iS2*em2'));
ett10=pmat*ett11;
ett11=ett10.*[neta1;neta2];
fit=sum(ett11);
ett11=(ett11)/fit;
filter(j,1:2)=ett11';
lik=lik+log(fit);
end
check=-1;
while check<0
S=zeros(T,1);
p1=filter(T,1);
p2=filter(T,2);
p=p1/(p1+p2);
u=rand(1,1);
S(T,1)=(u>=p);
for t=T-1:-1:1
if S(t+1)==0
p00=pmat(1,1)*filter(t,1);
p01=pmat(1,2)*filter(t,2);
elseif S(t+1)==1
p00=pmat(2,1)*filter(t,1);
p01=pmat(2,2)*filter(t,2);
end
u=rand(1,1);
p=p00/(p00+p01);
if u<p
S(t)=0;
else
S(t)=1;
end
end
if sum(S==0)>=ncrit && sum(S==1)>=ncrit
check=1;
end
end
ett11= [1;0];
iS1=1/sig1;
iS2=1/sig2;
dsig1=sqrt(sig1);
dsig2=sqrt(sig2);
filterx=zeros(T,2);
filterx(1,:)=ett11';
for j=2:T
if S(j)==0
phi1x=phi1;
phi2x=phi1;
else
phi1x=phi2;
phi2x=phi2;
end
em1=y(j)-x(j,:)*phi1x;
em2=y(j)-x(j,:)*phi2x;
neta1=(1/dsig1)*exp(-0.5*(em1*iS1*em1'));
neta2=(1/dsig2)*exp(-0.5*(em2*iS2*em2'));
ett10=qmat*ett11;
ett11=ett10.*[neta1;neta2];
fit=sum(ett11);
ett11=(ett11)/fit;
filterx(j,1:2)=ett11';
end
checkx=-1;
while checkx<0
VV=zeros(T,1);
p1=filterx(T,1);
p2=filterx(T,2);
p=p1/(p1+p2);
u=rand(1,1);
VV(T,1)=(u>=p);
for t=T-1:-1:1
if VV(t+1)==0
p00=qmat(1,1)*filterx(t,1);
p01=qmat(1,2)*filterx(t,2);
elseif VV(t+1)==1
p00=qmat(2,1)*filterx(t,1);
p01=qmat(2,2)*filterx(t,2);
end
u=rand(1,1);
p=p00/(p00+p01);
if u<p
VV(t)=0;
else
VV(t)=1;
end
end
if sum(VV==0)>=ncrit && sum(VV==1)>=ncrit
checkx=1;
end
end
tranmat=switchg(S+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);
pmat=[p 1-q;1-p q];
tranmatx=switchg(VV+1,[1;2]);
N00x=tranmat(1,1);
N01x=tranmat(1,2);
p0=drchrnd([N00x+v00;N01x+v01]);
px=p0(1,1);
qmat=[px 0;1-px 1];
sigmat=(VV==0).*sig1+(VV==1).*sig2;
sigmat1=sigmat(S==0);
sigmat2=sigmat(S==1);
id=find(S==0);
y1=y(id)./sqrt(sigmat1);
x1=x(id,:)./(repmat(sqrt(sigmat1),1,2));
M=inv(inv(Sigma0)+(x1'*x1))*(inv(Sigma0)*B0+x1'*y1);
V=inv(inv(Sigma0)+(x1'*x1));
phi1=M+(randn(1,2)*chol(V))';
id=find(S==1);
y2=y(id)./sqrt(sigmat2);
x2=x(id,:)./(repmat(sqrt(sigmat2),1,2));
M=inv(inv(Sigma0)+(x2'*x2))*(inv(Sigma0)*B0+x2'*y2);
V=inv(inv(Sigma0)+(x2'*x2));
phi2=M+(randn(1,2)*chol(V))';
residuals=(y-x*phi1).*(S==0)+(y-x*phi2).*(S==1);
e1=residuals(VV==0);
T1=v0+rows(e1);
D1=d0+e1'*e1;
z0=randn(T1,1);
z0z0=z0'*z0;
sig1=D1/z0z0;
e2=residuals(VV==1);
T2=v0+rows(e2);
D2=d0+e2'*e2;
z0=randn(T2,1);
z0z0=z0'*z0;
sig2=D2/z0z0;
if igibbs>BURN
chck=phi1(2,1)>phi2(2,1);
if chck
out1=[out1;([phi1' phi2'])];
out2=[out2;([sig1 sig2 ])];
out3=[out3;S'];
out4=[out4;[p q px]];
out5=[out5;VV'];
count=count+1;
end
end
igibbs=igibbs+1;
disp(sprintf(' Replication %s , %s Saved Draws %s. ', ...
num2str(igibbs), num2str(count) ));
end
figure(1)
subplot(6,2,1);
hist(out1(:,1),50);
vline(B1)
title('Coefficient regime 1');
axis tight
subplot(6,2,2);
hist(out1(:,3),50);
title('Coefficient regime 2');
vline(B2)
axis tight
subplot(6,2,3);
hist(out1(:,2),50);
vline(C1)
title('Intercept regime 1');
axis tight
subplot(6,2,4);
hist(out1(:,4),50);
title('Intercept regime 2');
vline(C2)
axis tight
subplot(6,2,5);
hist(out2(:,1),50);
vline(S1)
title('\sigma_{1}');
axis tight
subplot(6,2,6);
hist(out2(:,2),50);
vline(S2)
title('\sigma_{2}');
axis tight
subplot(6,2,7);
hist(out4(:,1),50);
title('P_{00}');
vline(P(1,1))
axis tight
subplot(6,2,8);
hist(out4(:,2),50);
title('p_{11}');
vline(P(2,2))
axis tight
subplot(6,2,9);
hist(out4(:,3),50);
title('q_{00}');
vline(Q(1,1))
axis tight
subplot(6,2,10)
temp=mean(out3,1);
plot(temp,'c','LineWidth',2);
hold on
plot(strue(:,2),'k','LineWidth',2)
title('Probability of Regime 1');
legend('Estimate','True')
axis tight
subplot(6,2,11)
temp=mean(out5,1);
plot(temp,'c','LineWidth',2);
hold on
plot(vtrue(:,2),'k','LineWidth',2)
title('Probability of Regime 1 (Variance)');
legend('Estimate','True')
axis tight