109 lines
3.9 KiB
Matlab
109 lines
3.9 KiB
Matlab
function dataset_info=var_sample_moments(nlag, var_trend_order, dataset_, dataset_info)
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% dataset_info=var_sample_moments(nlag, var_trend_order, dataset_, dataset_info)
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% Computes the sample moments of a VAR model.
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%
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% The VAR(p) model is defined by:
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%
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% y_t = \sum_{k=1}^p y_{t-k} A_k + z_t C + e_t for t = 1,...,T
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%
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% where y_t is a 1*m vector of observed endogenous variables, p is the
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% number of lags, A_k is an m*m real matrix, z_t is a 1*q vector of
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% exogenous (deterministic) variables, C is a q*m real matrix and
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% e_t is a vector of exogenous stochastic shocks. T is the number
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% of observations. The deterministic exogenous variables are assumed to
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% be a polynomial trend of order q = "var_trend_order".
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%
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% We define:
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%
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% <> Y = (y_1',y_2',...,y_T')' a T*m matrix,
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%
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% <> x_t = (y_{t-1},y_{t-2},...,y_{t-p},z_t) a 1*(mp+q) row vector,
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%
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% <> X = (x_1',x_2',...,x_T')' a T*(mp+q) matrix,
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%
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% <> E = (e_1',e_2',...,e_T')' a T*m matrix and
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%
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% <> A = (A_1',A_2',...,A_p',C')' an (mp+q)*m matrix of coefficients.
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%
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% So that we can equivalently write the VAR(p) model using the following
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% matrix representation:
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%
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% Y = X * A +E
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%
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%
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% INPUTS
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% o nlag [integer] Number of lags in the VAR model.
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% o var_trend_order [integer] Order of the polynomial exogenous trend:
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% = -1 no constant and no linear trend,
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% = 0 constant and no linear trend,
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% = 1 constant and linear trend.
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% o dataset_ [dseries] The sample.
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% o dataset_info [structure] data set information
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%
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% OUTPUTS
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% dataset_info [structure] containing the following new fields
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% o mYY [double] Y'*Y an m*m matrix.
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% o mXY [double] X'*Y an (mp+q)*m matrix.
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% o mYX [double] Y'*X an m*(mp+q) matrix.
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% o mXX [double] X'*X an (mp+q)*(mp+q) matrix.
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% o Ydata [double] Y a T*m matrix.
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% o Xdata [double] X a T*(mp+q) matrix.
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%
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% SPECIAL REQUIREMENTS
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% None.
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% Copyright © 2007-2023 Dynare Team
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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 <https://www.gnu.org/licenses/>.
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LastObservation = dataset_.dates(end);
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FirstObservation = dataset_.dates(1)+nlag;
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NumberOfObservations = LastObservation-FirstObservation+1;
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NumberOfVariables = dataset_.vobs;
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if isequal(var_trend_order,-1)
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% No constant no linear trend case.
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X = zeros(NumberOfObservations,NumberOfVariables*nlag);
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elseif isequal(var_trend_order,0)
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% Constant and no linear trend case.
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X = ones(NumberOfObservations,NumberOfVariables*nlag+1);
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elseif isequal(var_trend_order,1)
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% Constant and linear trend case.
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X = ones(NumberOfObservations,NumberOfVariables*nlag+2);
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else
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error('Estimation::var_sample_moments: trend must be equal to -1,0 or 1!')
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end
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% I build matrices Y and X
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Y = dataset_(FirstObservation:LastObservation).data;
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for t=1:NumberOfObservations
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currentdate = FirstObservation+(t-1);
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for lag = 1:nlag
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X(t,(lag-1)*NumberOfVariables+1:lag*NumberOfVariables) = dataset_(currentdate-lag).data;
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end
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end
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if (var_trend_order == 1)
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X(:,end) = transpose(1:NumberOfObservations);
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end
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dataset_info.mYY=Y'*Y;
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dataset_info.mYX=Y'*X;
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dataset_info.mXY=X'*Y;
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dataset_info.mXX=X'*X;
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dataset_info.Ydata=Y;
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dataset_info.Xdata=X; |