becmf.m

计量工具箱

function ylevf = becmf(y,nlag,nfor,begf,tight,weight,decay,r);
% PURPOSE: estimates a Bayesian error correction model of order n
%          and produces f-step-ahead forecasts
%---------------------------------------------------------------
% USAGE:    yfor = becmf(y,nlag,nfor,begf,tight,weight,decay,r)
% where:    y    = an (nobs x neqs) matrix of y-vectors in levels
%           nlag = the lag length
%           nfor = the forecast horizon
%           begf = the beginning date of the forecast
%          tight = Litterman's tightness hyperparameter
%         weight = Litterman's symmetric weight (scalar)
%          decay = Litterman's lag decay = lag^(-decay) 
%              r = # of co-integrating relations to use
%                  (optional: this will be determined using
%                  Johansen's trace test at 95%-level if left blank)                                    
%---------------------------------------------------------------
% NOTES: - constant vector automatically included
%        - x-matrix of exogenous variables not allowed
%        - error correction variables are automatically
%          constructed using output from Johansen's ML-estimator               
%---------------------------------------------------------------
% RETURNS:
%  yfor = an nfor x neqs matrix of level forecasts for each equation
%---------------------------------------------------------------
% SEE ALSO: bvarf, ecmf, varf, rvarf, recmf
%---------------------------------------------------------------

% written by:
% James P. LeSage, Dept of Economics
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% [e-mail]


[nobs neqs] = size(y);
% adjust nobs to feed the lags
nmin = min(nobs,begf-1);
nobse = nmin - nlag;

% do some error checking 

if nlag < 1
error('Lag length less than 1 in becmf');
end;

if nlag > nobs
error('Lag length exceeds observations in becmf');
end;

if decay < 0
error('Negative lag decay in becmf');
end;

[wchk1 wchk2] = size(weight);
if (wchk1 ~= wchk2) 
 error('non-square weight matrix in becmf');
elseif wchk1 > 1
 if wchk1 ~= neqs
 error('wrong size weight matrix in becmf');
 end;
end;

% check for zeros in weight matrix
if wchk1 == 1
  if weight == 0
  error('becmf: must have weight > 0');
  end;
elseif wchk1 > 1
  zip = find(weight == 0);
 if length(zip) ~= 0
 error('becmf: must have weights > 0');
 end;
end;



nx = 0;

  if nargin == 8 % user supplied r-value
 % use johansen to determine ec variables
 % decrement r by 1 when calling johansen
 jres = johansen(y(1:nmin,:),0,nlag);
 % recover error correction vectors
 ecvectors = jres.evec;
        index = jres.ind; 
 % construct r-error correction variables
 x = mlag(y(1:nmin,index),1)*ecvectors(:,1:r); 
   [nobs2 nx] = size(x);
  elseif nargin == 7 % we have to determine r-value
 jres = johansen(y(1:nmin,:),0,nlag);
 % find r = # significant co-integrating relations using
 % the trace statistic output
 trstat = jres.lr1;
 tsignf = jres.cvt;
 r = 0;
 for i=1:neqs;
  if trstat(i,1) > tsignf(i,2)
   r = i;
  end;
 end;
 % recover error correction vectors
 ecvectors = jres.evec;
        index = jres.ind; 
 % construct r error correction variables
 x = mlag(y(1:nmin,index),1)*ecvectors(:,1:r); 
   [nobs2 nx] = size(x); 
  else
   error('Wrong # of input arguments to becmf');
  end;


% adjust nvar for constant term and error correction terms
k = neqs*nlag+nx+1;

% truncate to begf-1 for estimation 
ytrunc = y(1:nmin,:);

% transform to 1st difference form
dy = zeros(nmin,neqs);
for i=1:neqs;
dy(:,i) = ytrunc(:,i) - lag(ytrunc(:,i),1);
end;

% generate lagged rhs matrix
xlag = mlag(dy,nlag);

% do scaling here using fuller y-vector information
% determine scale factors using univariate AR model

scale = zeros(neqs,1);
scale2 = zeros(neqs,neqs);
ytmp = zeros(nmin,1);

for j=1:neqs
 ytmp = dy(1:nmin,j);
 scale(j,1) = scstd(ytmp,nmin,nlag);
end;

for j=1:neqs;
 for i=1:neqs;
 scale2(i,j) = scale(j)/scale(i);
 end;
end;

% add constant and ec variables to x-matrix and feed lags
if nx == 0
 xmat = [xlag(nlag+1:nmin,:) ones(nmin-nlag,1)];
else
 xmat = [xlag(nlag+1:nmin,:) x(nlag+1:nmin,:) ones(nmin-nlag,1)];
end;

% form xpx only once to save time
xpx = xmat'*xmat;

% dimension some result matrices
bmat = zeros(k,neqs);
yfor = zeros(nfor,neqs);
ylev = zeros(nfor,neqs);

% pull out each y-vector and run regressions

for j=1:neqs;

yvec = dy(nlag+1:nmin,j);
xpy = xmat'*yvec;

reslt = theilbf(xpy,xpx,nlag,neqs,j,tight,weight,decay,scale2,scale,nx);

bmat(:,j) = reslt.beta;

end;

% given bmat values generate future forecasts 
    
% 1-step-ahead forecast 
xtrunc = [dy(nmin-(nlag):nmin,:)
          zeros(1,neqs)];
xfor = mlag(xtrunc,nlag);
[xend junk] = size(xfor);
xobs = xfor(xend,:);
if nx > 0
ecterm = y(begf-1,index)*ecvectors(:,1:r); % add ec variables 
xvec = [xobs ecterm 1];
else
xvec = [xobs 1];
end;

% loop over equations
for i=1:neqs;
bhat = bmat(:,i);
yfor(1,i) = xvec*bhat; % NOTE this is a change forecast
ylev(1,i) = yfor(1,i) + y(nmin-1,i); % this adds the previous level
end;

xnew = zeros(nlag+nx+1,neqs);

% 2 through nlag-step-ahead forecasts
for step=2:nlag;

if step <= nfor;

xnew(1:nlag-step+1,:) = dy(nmin-nlag+step:nmin,:);
xnew(nlag-step+2:nlag,:) = yfor(1:step-1,:);
xnew(nlag+1,:) = zeros(1,neqs);


xfor = mlag(xnew,nlag);
[xend junk] = size(xfor);
xobs = xfor(xend,:);
% construct ec terms based on levels forecast from previous periods
if nx > 0
ecterm = ylev(step-1,index)*ecvectors(:,1:r);
xvec = [xobs ecterm 1];
else
xvec = [xobs 1];
end;


% loop over equations
for i=1:neqs;
bhat = bmat(:,i);
yfor(step,i) = xvec*bhat; % change forecast
ylev(step,i) = yfor(step,i) + ylev(step-1,i); % level forecast
end;

end;

end;

% nlag through nfore-step-ahead forecasts
for step=nlag:nfor-1;

if step <= nfor;

cnt = step-(nlag-1);

 for i=1:nlag;
  xnew(i,:) = yfor(cnt,:);
  cnt = cnt+1;
 end;
 
xfor = mlag(xnew,nlag);
[xend junk] = size(xfor);
xobs = xfor(xend,:);
% construct ec terms based on levels forecast from previous periods
if nx > 0
ecterm = ylev(step,index)*ecvectors(:,1:r);
xvec = [xobs ecterm 1];
else
xvec = [xobs 1];
end;


% loop over equations
for i=1:neqs;
bhat = bmat(:,i);
yfor(step+1,i) = xvec*bhat; % change forecast
ylev(step+1,i) = yfor(step+1,i) + ylev(step-1,i); % level forecast
end;

end;

end;
  
% convert 1st difference forecasts to levels
ylevf = zeros(nfor,neqs);
% 1-step-ahead forecast
ylevf(1,:) = yfor(1,:) + y(begf-1,:); % add change to actual from time t;
% 2-nfor-step-ahead forecasts
for i=2:nfor % 
ylevf(i,:) = yfor(i,:) + ylevf(i-1,:);
end;