165 lines
6.8 KiB
Matlab
165 lines
6.8 KiB
Matlab
function [xtx,xty,yty,fss,phi,y,ncoef,xr,Bh,e] = fn_dataxy(nvar,lags,z,mu,indxDummy,nexo)
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% [xtx,xty,yty,fss,phi,y,ncoef,xr,Bh,e] = fn_dataxy(nvar,lags,z,mu,indxDummy,nexo)
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%
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% Export arranged data matrices for future estimation of the VAR.
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% If indxDummy=0, no mu's are used at all and Bh is the OLS estimate.
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% If indxDummy=1, only mu(5) and mu(6) as dummy observations. See fn_rnrprior*.m for using mu(1)-mu(4).
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% See Wagonner and Zha's Gibbs sampling paper.
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%
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% nvar: number of endogenous variables.
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% lags: the maximum length of lag
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% z: T*(nvar+(nexo-1)) matrix of raw or original data (no manipulation involved)
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% with sample size including lags and with exogenous variables other than a constant.
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% Order of columns: (1) nvar endogenous variables; (2) (nexo-1) exogenous variables;
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% (3) constants will be automatically put in the last column.
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% mu: 6-by-1 vector of hyperparameters (the following numbers for Atlanta Fed's forecast), where
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% only mu(5) and mu(6) are used for dummy observations in this function (i.e.,
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% mu(1)-mu(4) are irrelevant here). See fn_rnrprior*.m for using mu(1)-mu(4).
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% mu(1): overall tightness and also for A0; (0.57)
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% mu(2): relative tightness for A+; (0.13)
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% mu(3): relative tightness for the constant term; (0.1)
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% mu(4): tightness on lag decay; (1)
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% mu(5): weight on nvar sums of coeffs dummy observations (unit roots); (5)
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% mu(6): weight on single dummy initial observation including constant
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% (cointegration, unit roots, and stationarity); (5)
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% indxDummy: 1: add dummy observations to the data; 0: no dummy added.
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% nexo: number of exogenous variables. The constant term is the default setting. Besides this term,
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% we have nexo-1 exogenous variables. Optional. If left blank, nexo is set to 1.
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% -------------------
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% xtx: X'X: k-by-k where k=ncoef
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% xty: X'Y: k-by-nvar
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% yty: Y'Y: nvar-by-nvar
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% fss: T: sample size excluding lags. With dummyies, fss=nSample-lags+ndobs.
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% phi: X; T-by-k; column: [nvar for 1st lag, ..., nvar for last lag, other exogenous terms, const term]
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% y: Y: T-by-nvar where T=fss
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% ncoef: number of coefficients in *each* equation. RHS coefficients only, nvar*lags+nexo
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% xr: the economy size (ncoef-by-ncoef) in qr(phi) so that xr=chol(X'*X) or xr'*xr=X'*X
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% Bh: ncoef-by-nvar estimated reduced-form parameter; column: nvar;
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% row: ncoef=[nvar for 1st lag, ..., nvar for last lag, other exogenous terms, const term]
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% e: estimated residual e = y -x*Bh, T-by-nvar
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%
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% Tao Zha, February 2000.
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% Copyright (C) 2000-2011 Tao Zha
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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if nargin == 5
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nexo=1; % default for constant term
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elseif nexo<1
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error('We need at least one exogenous term so nexo must >= 1')
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end
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%*** original sample dimension without dummy prior
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nSample = size(z,1); % the sample size (including lags, of course)
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sb = lags+1; % original beginning without dummies
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ncoef = nvar*lags+nexo; % number of coefficients in *each* equation, RHS coefficients only.
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if indxDummy % prior dummy prior
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%*** expanded sample dimension by dummy prior
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ndobs=nvar+1; % number of dummy observations
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fss = nSample+ndobs-lags;
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%
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% **** nvar prior dummy observations with the sum of coefficients
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% ** construct X for Y = X*B + U where phi = X: (T-lags)*k, Y: (T-lags)*nvar
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% ** columns: k = # of [nvar for 1st lag, ..., nvar for last lag, exo var, const]
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% ** Now, T=T+ndobs -- added with "ndobs" dummy observations
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%
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phi = zeros(fss,ncoef);
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%* constant term
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const = ones(fss,1);
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const(1:nvar) = zeros(nvar,1);
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phi(:,ncoef) = const; % the first nvar periods: no or zero constant!
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%* other exogenous (than) constant term
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phi(ndobs+1:end,ncoef-nexo+1:ncoef-1) = z(lags+1:end,nvar+1:nvar+nexo-1);
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exox = zeros(ndobs,nexo);
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phi(1:ndobs,ncoef-nexo+1:ncoef-1) = exox(:,1:nexo-1);
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% this = [] when nexo=1 (no other exogenous than constant)
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xdgel = z(:,1:nvar); % endogenous variable matrix
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xdgelint = mean(xdgel(1:lags,:),1); % mean of the first lags initial conditions
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%* Dummies
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for k=1:nvar
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for m=1:lags
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phi(ndobs,nvar*(m-1)+k) = xdgelint(k);
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phi(k,nvar*(m-1)+k) = xdgelint(k);
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% <<>> multiply hyperparameter later
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end
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end
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%* True data
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for k=1:lags
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phi(ndobs+1:fss,nvar*(k-1)+1:nvar*k) = xdgel(sb-k:nSample-k,:);
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% row: T-lags; column: [nvar for 1st lag, ..., nvar for last lag, exo var, const]
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% Thus, # of columns is nvar*lags+nexo = ncoef.
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end
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%
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% ** Y with "ndobs" dummies added
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y = zeros(fss,nvar);
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%* Dummies
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for k=1:nvar
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y(ndobs,k) = xdgelint(k);
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y(k,k) = xdgelint(k);
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% multiply hyperparameter later
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end
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%* True data
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y(ndobs+1:fss,:) = xdgel(sb:nSample,:);
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phi(1:nvar,:) = 1*mu(5)*phi(1:nvar,:); % standard Sims and Zha prior
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y(1:nvar,:) = mu(5)*y(1:nvar,:); % standard Sims and Zha prior
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phi(nvar+1,:) = mu(6)*phi(nvar+1,:);
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y(nvar+1,:) = mu(6)*y(nvar+1,:);
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[xq,xr]=qr(phi,0);
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xtx=xr'*xr;
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xty=phi'*y;
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[yq,yr]=qr(y,0);
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yty=yr'*yr;
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Bh = xr\(xr'\xty); % xtx\xty where inv(X'X)*(X'Y)
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e=y-phi*Bh;
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else
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fss = nSample-lags;
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%
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% ** construct X for Y = X*B + U where phi = X: (T-lags)*k, Y: (T-lags)*nvar
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% ** columns: k = # of [nvar for 1st lag, ..., nvar for last lag, exo var, const]
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%
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phi = zeros(fss,ncoef);
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%* constant term
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const = ones(fss,1);
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phi(:,ncoef) = const; % the first nvar periods: no or zero constant!
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%* other exogenous (than) constant term
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phi(:,ncoef-nexo+1:ncoef-1) = z(lags+1:end,nvar+1:nvar+nexo-1);
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% this = [] when nexo=1 (no other exogenous than constant)
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xdgel = z(:,1:nvar); % endogenous variable matrix
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%* True data
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for k=1:lags
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phi(:,nvar*(k-1)+1:nvar*k) = xdgel(sb-k:nSample-k,:);
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% row: T-lags; column: [nvar for 1st lag, ..., nvar for last lag, exo var, const]
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% Thus, # of columns is nvar*lags+nexo = ncoef.
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end
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%
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y = xdgel(sb:nSample,:);
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[xq,xr]=qr(phi,0);
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xtx=xr'*xr;
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xty=phi'*y;
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[yq,yr]=qr(y,0);
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yty=yr'*yr;
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Bh = xr\(xr'\xty); % xtx\xty where inv(X'X)*(X'Y)
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e=y-phi*Bh;
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end
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