%BAYES_DFM?This?implements?the?state-space?estimation?of?the?dynamic
%factors?their?loadings?and?autoregressive?parameters.?The?program?was
%written?by?Piotr?Eliasz?（2003）?Princeton?University?for?his?PhD?thesis?and
%and?used?in?Bernake?Boivin?and?Eliasz?（2005）?published?in?QJE.
%Modified?by?Dimitris?Korobilis?on?Monday?June?11?2007
%--------------------------------------------------------------------------
%?Estimate?dynamic?factor?model:
%????????????????X_t?=?Lam?x?F_t?+?e_t
%????????????????F_t?=?B（L）?x?F_t-1?+?u_t
%?The?previous?（Eliasz?2005）?version?was:
%?????????[X_t?;?Y_t]?=?[Lf?Ly?;?0?I]?x?[F_t?;?Y_t]?+?e_t
%?????????[F_t?;?Y_t]?=?[B（L）?;?0?I]?x?[F_t-1?;?Y_t-1]?+?u_t
%
%--------------------------------------------------------------------------

clear?all;
clc;
randn（‘seed‘sum（100*clock））;?%#ok<*RAND>
rand（‘seed‘sum（100*clock））;
%---------------------------LOAD?DATA--------------------------------------
%?simulated?dataset
X=dfmdgp（）;

[TN]=size（X）;
%Demean?xraw
X=X-repmat（mean（X）T1）;

%?Number?of?factors?&?lags?in?B（L）:
K=3;
lags=1;
%----------------------------PRELIMINARIES---------------------------------
%?Set?some?Gibbs?-?related?preliminaries
nods?=?10000;??%?Number?of?draws
bid?=?2000;???%?Number?of?burn-in-draws
thin?=?1;???%?Consider?every?thin-th?draw?（thin?value）

%?store?draws?in:
Ldraw=zeros（nods-bidNK）;
Bdraw=zeros（nods-bidKKlags）;
Qdraw=zeros（nods-bidKK）;
Fdraw=zeros（nods-bidTK）;??
%********************************************************
%?STANDARDIZE?for?PC?only
X_st=X./repmat（std（X1）T1）;
%?First?step?-?extract?PC?from?X
[F0Lf]=extract（X_stK）;
%?Transform?factors?and?loadings?for?LE?normalization
[qlrl]=qr（Lf‘）;
Lf=rl;??%?do?not?transpose?yet?is?upper?triangular
F0=F0*ql;
%?Need?identity?in?the?first?K?columns?of?Lf?call?them?A?for?now
A=Lf（:1:K）;
Lf=[eye（K）inv（A）*Lf（:（K+1）:N）]‘;
F0=F0*A;
%?Obtain?R:
e=X_st-F0*Lf‘;
R=e‘*e./T;
R=diag（diag（R））;
L=Lf;
%?Run?a?VAR?in?F?obtain?initial?B?and?Q
[BBcvQinvFF]=estvar（F0lags[]）;

%?Put?it?all?in?state-space?representation?write?obs?equ?as?XY=FY*L+e
XY=X;???%Tx（N+M）
FY=F0;

%?adjust?for?lags?in?state?equation?Q?is?KxK
Q=[Q?zeros（KK*（lags-1））;zeros（K*（lags-1）K*lags）];
B=[B（::）;eye（K*（lags-1））?zeros（K*（lags-1）K）];

%?start?with
Sp=zeros（K*lags1）;
Pp=eye（K*lags）;??

%?Proper?Priors:-----------------------------------------------------------
%?on?VAR?--?Normal-Wishart?after?Kadiyala?Karlsson?1997
%?on?Q?--?si
%?on?B?--?increasing?tightness
%?on?observable?equation:
%?N（0I）-iG（30.001）

%?prior?distributions?for?VAR?part?need?B?and?Q
vo=K+2;
s0=3;
alpha=0.001;
L_var_prior=eye（K）;
Qi=zeros（K1）;

%?singles?out?latent?factors
indexnM=ones（Klags）;
indexnM=find（indexnM==1）;
%***************End?of?Preliminaries?&?PriorSpecification******************

tic;
%==========================================================================
%==========================?Start?Sampling?================================
%=====================================

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2009-09-23?11:53??Factor_Models\
?????文件????????7383??2009-08-09?13:35??Factor_Models\BAYES_DFM.m
?????文件?????????706??2009-06-24?02:13??Factor_Models\bernoullirnd.m
?????文件????????3214??2009-06-24?02:31??Factor_Models\BFM.m
?????文件?????????479??2009-07-07?00:16??Factor_Models\bfmdgp.m
?????文件?????????305??2009-05-29?23:09??Factor_Models\bfmdgp2.m
?????文件?????????884??2009-05-29?23:24??Factor_Models\dfmdgp.m
?????文件????????1042??2007-06-20?20:08??Factor_Models\estvar.m
?????文件?????????527??2004-07-31?17:23??Factor_Models\extract.m
?????文件?????????677??2004-12-29?13:22??Factor_Models\gamrnd.m
?????文件??????294074??2007-06-01?12:28??Factor_Models\Lopez+West?（2004）?-?BAYESIAN?MODEL?ASSESSMENT?IN?FACTOR?ANALYSIS.pdf
?????文件????????1335??2009-05-29?23:25??Factor_Models\mlag.m
?????文件????????1830??2004-07-31?17:23??Factor_Models\mvnrnd.m
?????文件????????1059??2009-05-29?23:14??Factor_Models\normlt_rnd.m
?????文件????????1827??2009-05-29?23:15??Factor_Models\normt_rnd.m
?????文件?????????281??2004-07-31?17:23??Factor_Models\olssvd.m