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function var_sample_moments(nlag, var_trend_order, dataset_)%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 nlag [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.
% o dataset_ [dseries] The sample.
%
% 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.
%
% REMARKS
% Outputs are saved in the base workspace (not returned by the function).
% Copyright (C) 2007-2014 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/>.
LastObservation = dataset_.dates(end);
FirstObservation = dataset_.dates(1)+nlag;
NumberOfObservations = LastObservation-FirstObservation+1;
NumberOfVariables = dataset_.vobs;
if isequal(var_trend_order,-1)
% No constant no linear trend case.
X = zeros(NumberOfObservations,NumberOfVariables*nlag);
elseif isequal(var_trend_order,0)
% Constant and no linear trend case.
X = ones(NumberOfObservations,NumberOfVariables*nlag+1);
indx = NumberOfVariables*nlag+1;
elseif isequal(var_trend_order,1)
% Constant and linear trend case.
X = ones(NumberOfObservations,NumberOfVariables*nlag+2);
indx = NumberOfVariables*nlag+1:NumberOfVariables*nlag+2;
else
error('Estimation::var_sample_moments: trend must be equal to -1,0 or 1!')
return
end
% I build matrices Y and X
Y = dataset_(FirstObservation:LastObservation).data;
for t=1:NumberOfObservations
currentdate = FirstObservation+(t-1);
for lag = 1:nlag
X(t,(lag-1)*NumberOfVariables+1:lag*NumberOfVariables) = dataset_(currentdate-lag).data;
end
end
if (var_trend_order == 1)
X(:,end) = transpose(1:NumberOfObservations)
end
assignin('base', 'mYY', Y'*Y);
assignin('base', 'mYX', Y'*X);
assignin('base', 'mXY', X'*Y);
assignin('base', 'mXX', X'*X);
assignin('base', 'Ydata', Y);
assignin('base', 'Xdata', X);
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