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ConfigFile.hh

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  • fn_dataxy.m 6.28 KiB
    function [xtx,xty,yty,fss,phi,y,ncoef,xr,Bh,e] = fn_dataxy(nvar,lags,z,mu,indxDummy,nexo)
    % [xtx,xty,yty,fss,phi,y,ncoef,xr,Bh,e] = fn_dataxy(nvar,lags,z,mu,indxDummy,nexo)
    %
    %    Export arranged data matrices for future estimation of the VAR.
    %    If indxDummy=0, no mu's are used at all and Bh is the OLS estimate.
    %    If indxDummy=1, only mu(5) and mu(6) as dummy observations.  See fn_rnrprior*.m for using mu(1)-mu(4).
    %    See Wagonner and Zha's Gibbs sampling paper.
    %
    % nvar:  number of endogenous variables.
    % lags: the maximum length of lag
    % z: T*(nvar+(nexo-1)) matrix of raw or original data (no manipulation involved)
    %       with sample size including lags and with exogenous variables other than a constant.
    %       Order of columns: (1) nvar endogenous variables; (2) (nexo-1) exogenous variables;
    %                         (3) constants will be automatically put in the last column.
    % mu: 6-by-1 vector of hyperparameters (the following numbers for Atlanta Fed's forecast), where
    %         only mu(5) and mu(6) are used for dummy observations in this function (i.e.,
    %         mu(1)-mu(4) are irrelevant here).  See fn_rnrprior*.m for using mu(1)-mu(4).
    %       mu(1): overall tightness and also for A0;  (0.57)
    %       mu(2): relative tightness for A+;  (0.13)
    %       mu(3): relative tightness for the constant term;  (0.1)
    %       mu(4): tightness on lag decay;  (1)
    %       mu(5): weight on nvar sums of coeffs dummy observations (unit roots);  (5)
    %       mu(6): weight on single dummy initial observation including constant
    %               (cointegration, unit roots, and stationarity);  (5)
    % indxDummy:  1: add dummy observations to the data; 0: no dummy added.
    % nexo:  number of exogenous variables.  The constant term is the default setting. Besides this term,
    %              we have nexo-1 exogenous variables.  Optional.  If left blank, nexo is set to 1.
    % -------------------
    % xtx:  X'X: k-by-k where k=ncoef
    % xty:  X'Y: k-by-nvar
    % yty:  Y'Y: nvar-by-nvar
    % fss:  T: sample size excluding lags.  With dummyies, fss=nSample-lags+ndobs.
    % phi:  X; T-by-k; column: [nvar for 1st lag, ..., nvar for last lag, other exogenous terms, const term]
    % y:    Y: T-by-nvar where T=fss
    % ncoef: number of coefficients in *each* equation. RHS coefficients only, nvar*lags+nexo
    % xr:  the economy size (ncoef-by-ncoef) in qr(phi) so that xr=chol(X'*X) or xr'*xr=X'*X
    % Bh: ncoef-by-nvar estimated reduced-form parameter; column: nvar;
    %      row: ncoef=[nvar for 1st lag, ..., nvar for last lag, other exogenous terms, const term]
    % e:  estimated residual e = y -x*Bh,  T-by-nvar
    %
    % Tao Zha, February 2000.
    
    if nargin == 5
       nexo=1;    % default for constant term
    elseif nexo<1
       error('We need at least one exogenous term so nexo must >= 1')
    end
    
    %*** original sample dimension without dummy prior
    nSample = size(z,1); % the sample size (including lags, of course)
    sb = lags+1;   % original beginning without dummies
    ncoef = nvar*lags+nexo;  % number of coefficients in *each* equation, RHS coefficients only.
    
    if indxDummy   % prior dummy prior
       %*** expanded sample dimension by dummy prior
       ndobs=nvar+1;         % number of dummy observations
       fss = nSample+ndobs-lags;
    
       %
       % **** nvar prior dummy observations with the sum of coefficients
       % ** construct X for Y = X*B + U where phi = X: (T-lags)*k, Y: (T-lags)*nvar
       % **    columns: k = # of [nvar for 1st lag, ..., nvar for last lag, exo var, const]
       % **    Now, T=T+ndobs -- added with "ndobs" dummy observations
       %
       phi = zeros(fss,ncoef);
       %* constant term
       const = ones(fss,1);
       const(1:nvar) = zeros(nvar,1);
       phi(:,ncoef) = const;      % the first nvar periods: no or zero constant!
       %* other exogenous (than) constant term
       phi(ndobs+1:end,ncoef-nexo+1:ncoef-1) = z(lags+1:end,nvar+1:nvar+nexo-1);
       exox = zeros(ndobs,nexo);
       phi(1:ndobs,ncoef-nexo+1:ncoef-1) = exox(:,1:nexo-1);
                % this = [] when nexo=1 (no other exogenous than constant)
    
       xdgel = z(:,1:nvar);  % endogenous variable matrix
       xdgelint = mean(xdgel(1:lags,:),1); % mean of the first lags initial conditions
       %* Dummies
       for k=1:nvar
          for m=1:lags
             phi(ndobs,nvar*(m-1)+k) = xdgelint(k);
             phi(k,nvar*(m-1)+k) = xdgelint(k);
             % <<>> multiply hyperparameter later
          end
       end
       %* True data
       for k=1:lags
          phi(ndobs+1:fss,nvar*(k-1)+1:nvar*k) = xdgel(sb-k:nSample-k,:);
          % row: T-lags; column: [nvar for 1st lag, ..., nvar for last lag, exo var, const]
          %                     Thus, # of columns is nvar*lags+nexo = ncoef.
       end
       %
       % ** Y with "ndobs" dummies added
       y = zeros(fss,nvar);
       %* Dummies
       for k=1:nvar
          y(ndobs,k) = xdgelint(k);
          y(k,k) = xdgelint(k);
          % multiply hyperparameter later
       end
       %* True data
       y(ndobs+1:fss,:) = xdgel(sb:nSample,:);
    
       phi(1:nvar,:) = 1*mu(5)*phi(1:nvar,:);    % standard Sims and Zha prior
       y(1:nvar,:) = mu(5)*y(1:nvar,:);      % standard Sims and Zha prior
       phi(nvar+1,:) = mu(6)*phi(nvar+1,:);
       y(nvar+1,:) = mu(6)*y(nvar+1,:);
    
       [xq,xr]=qr(phi,0);
       xtx=xr'*xr;
       xty=phi'*y;
       [yq,yr]=qr(y,0);
       yty=yr'*yr;
       Bh = xr\(xr'\xty);   % xtx\xty where inv(X'X)*(X'Y)
       e=y-phi*Bh;
    else
       fss = nSample-lags;
       %
       % ** construct X for Y = X*B + U where phi = X: (T-lags)*k, Y: (T-lags)*nvar
       % **    columns: k = # of [nvar for 1st lag, ..., nvar for last lag, exo var, const]
       %
       phi = zeros(fss,ncoef);
       %* constant term
       const = ones(fss,1);
       phi(:,ncoef) = const;      % the first nvar periods: no or zero constant!
       %* other exogenous (than) constant term
       phi(:,ncoef-nexo+1:ncoef-1) = z(lags+1:end,nvar+1:nvar+nexo-1);
                % this = [] when nexo=1 (no other exogenous than constant)
    
       xdgel = z(:,1:nvar);  % endogenous variable matrix
       %* True data
       for k=1:lags
          phi(:,nvar*(k-1)+1:nvar*k) = xdgel(sb-k:nSample-k,:);
          % row: T-lags; column: [nvar for 1st lag, ..., nvar for last lag, exo var, const]
          %                     Thus, # of columns is nvar*lags+nexo = ncoef.
       end
       %
       y = xdgel(sb:nSample,:);
    
       [xq,xr]=qr(phi,0);
       xtx=xr'*xr;
       xty=phi'*y;
       [yq,yr]=qr(y,0);
       yty=yr'*yr;
       Bh = xr\(xr'\xty);   % xtx\xty where inv(X'X)*(X'Y)
       e=y-phi*Bh;
    end