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function [YtY,XtY,YtX,XtX,Y,X] = ...
var_sample_moments(FirstObservation,LastObservation,qlag,var_trend_order,datafile,varobs,xls_sheet,xls_range)
% Computes the sample moments of a VAR model.
%
% The VAR(p) model is defined by:
%
% y_t = \sum_{k=1}^p y_{t-k} A_k + z_t C + e_t for t = 1,...,T
%
% where y_t is a 1*m vector of observed endogenous variables, p is the
% number of lags, A_k is an m*m real matrix, z_t is a 1*q vector of
% exogenous (deterministic) variables, C is a q*m real matrix and
% e_t is a vector of exogenous stochastic shocks. T is the number
% of observations. The deterministic exogenous variables are assumed to
% be a polynomial trend of order q = "var_trend_order".
%
% We define:
%
% <> Y = (y_1',y_2',...,y_T')' a T*m matrix,
%
% <> x_t = (y_{t-1},y_{t-2},...,y_{t-p},z_t) a 1*(mp+q) row vector,
%
% <> X = (x_1',x_2',...,x_T')' a T*(mp+q) matrix,
%
% <> E = (e_1',e_2',...,e_T')' a T*m matrix and
%
% <> A = (A_1',A_2',...,A_p',C')' an (mp+q)*m matrix of coefficients.
%
% So that we can equivalently write the VAR(p) model using the following
% matrix representation:
%
% Y = X * A +E
%
%
% INPUTS
% o FirstObservation [integer] First observation.
% o LastObservation [integer] Last observation.
% o qlag [integer] Number of lags in the VAR model.
% o var_trend_order [integer] Order of the polynomial exogenous trend:
% = -1 no constant and no linear trend,
% = 0 constant and no linear trend,
% = 1 constant and linear trend.
%
% OUTPUTS
% o YtY [double] Y'*Y an m*m matrix.
% o XtY [double] X'*Y an (mp+q)*m matrix.
% o YtX [double] Y'*X an m*(mp+q) matrix.
% o XtX [double] X'*X an (mp+q)*(mp+q) matrix.
% o Y [double] Y a T*m matrix.
% o X [double] X a T*(mp+q) matrix.
%
% SPECIAL REQUIREMENTS
% None.
% Copyright (C) 2007-2009 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
X = [];
Y = [];
YtY = [];
YtX = [];
XtY = [];
XtX = [];
data = read_variables(datafile,varobs,[],xls_sheet,xls_range);
if qlag > FirstObservation
disp('VarSampleMoments :: not enough data to initialize! Try to increase FirstObservation.')
return
end
NumberOfObservations = LastObservation-FirstObservation+1;% This is T.
NumberOfVariables = size(varobs,1);% This is m.
if var_trend_order == -1% No constant no linear trend case.
X = zeros(NumberOfObservations,NumberOfVariables*qlag);
elseif var_trend_order == 0% Constant and no linear trend case.
X = ones(NumberOfObservations,NumberOfVariables*qlag+1);
indx = NumberOfVariables*qlag+1;
elseif var_trend_order == 1;% Constant and linear trend case.
X = ones(NumberOfObservations,NumberOfVariables*qlag+2);
indx = NumberOfVariables*qlag+1:NumberOfVariables*qlag+2;
else
disp('var_sample_moments :: trend must be equal to -1,0 or 1!')
return
end
% I build matrices Y and X
Y = data(FirstObservation:LastObservation,:);
for t=1:NumberOfObservations
line = t + FirstObservation-1;
for lag = 1:qlag
X(t,(lag-1)*NumberOfVariables+1:lag*NumberOfVariables) = data(line-lag,:);
end
end
if (var_trend_order == 1)
X(:,end) = transpose(1:NumberOfObservations)
end
YtY = Y'*Y;
YtX = Y'*X;
XtY = X'*Y;
XtX = X'*X;
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