1function var_sample_moments(nlag, var_trend_order, dataset_)%datafile,varobs,xls_sheet,xls_range)
2% Computes the sample moments of a VAR model.
3%
4% The VAR(p) model is defined by:
5%
6%   y_t = \sum_{k=1}^p y_{t-k} A_k + z_t C + e_t  for t = 1,...,T
7%
8% where y_t is a 1*m vector of observed endogenous variables, p is the
9% number of lags, A_k is an m*m real matrix, z_t is a 1*q vector of
10% exogenous (deterministic) variables, C is a q*m real matrix and
11% e_t is a vector of exogenous stochastic shocks. T is the number
12% of observations. The deterministic exogenous variables are assumed to
13% be a polynomial trend of order q = "var_trend_order".
14%
15% We define:
16%
17%  <>  Y = (y_1',y_2',...,y_T')' a T*m matrix,
18%
19%  <>  x_t = (y_{t-1},y_{t-2},...,y_{t-p},z_t) a 1*(mp+q) row vector,
20%
21%  <>  X = (x_1',x_2',...,x_T')' a T*(mp+q) matrix,
22%
23%  <>  E = (e_1',e_2',...,e_T')' a T*m matrix and
24%
25%  <>  A = (A_1',A_2',...,A_p',C')' an (mp+q)*m matrix of coefficients.
26%
27% So that we can equivalently write the VAR(p) model using the following
28% matrix representation:
29%
30%   Y = X * A +E
31%
32%
33% INPUTS
34%   o nlag                [integer] Number of lags in the VAR model.
35%   o var_trend_order     [integer] Order of the polynomial exogenous trend:
36%                                       = -1 no constant and no linear trend,
37%                                       =  0 constant and no linear trend,
38%                                       =  1 constant and linear trend.
39%   o dataset_            [dseries] The sample.
40%
41% OUTPUTS
42%   o YtY                 [double]  Y'*Y an m*m matrix.
43%   o XtY                 [double]  X'*Y an (mp+q)*m matrix.
44%   o YtX                 [double]  Y'*X an m*(mp+q) matrix.
45%   o XtX                 [double]  X'*X an (mp+q)*(mp+q) matrix.
46%   o Y                   [double]  Y a T*m matrix.
47%   o X                   [double]  X a T*(mp+q) matrix.
48%
49% SPECIAL REQUIREMENTS
50%   None.
51%
52% REMARKS
53%   Outputs are saved in the base workspace (not returned by the function).
54
55% Copyright (C) 2007-2014 Dynare Team
56%
57% This file is part of Dynare.
58%
59% Dynare is free software: you can redistribute it and/or modify
60% it under the terms of the GNU General Public License as published by
61% the Free Software Foundation, either version 3 of the License, or
62% (at your option) any later version.
63%
64% Dynare is distributed in the hope that it will be useful,
65% but WITHOUT ANY WARRANTY; without even the implied warranty of
66% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
67% GNU General Public License for more details.
68%
69% You should have received a copy of the GNU General Public License
70% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
71
72LastObservation = dataset_.dates(end);
73FirstObservation = dataset_.dates(1)+nlag;
74
75NumberOfObservations = LastObservation-FirstObservation+1;
76NumberOfVariables = dataset_.vobs;
77
78if isequal(var_trend_order,-1)
79    % No constant no linear trend case.
80    X = zeros(NumberOfObservations,NumberOfVariables*nlag);
81elseif isequal(var_trend_order,0)
82    % Constant and no linear trend case.
83    X = ones(NumberOfObservations,NumberOfVariables*nlag+1);
84    indx = NumberOfVariables*nlag+1;
85elseif isequal(var_trend_order,1)
86    % Constant and linear trend case.
87    X = ones(NumberOfObservations,NumberOfVariables*nlag+2);
88    indx = NumberOfVariables*nlag+1:NumberOfVariables*nlag+2;
89else
90    error('Estimation::var_sample_moments: trend must be equal to -1,0 or 1!')
91    return
92end
93
94% I build matrices Y and X
95Y = dataset_(FirstObservation:LastObservation).data;
96
97for t=1:NumberOfObservations
98    currentdate = FirstObservation+(t-1);
99    for lag = 1:nlag
100        X(t,(lag-1)*NumberOfVariables+1:lag*NumberOfVariables) = dataset_(currentdate-lag).data;
101    end
102end
103
104if (var_trend_order == 1)
105    X(:,end) = transpose(1:NumberOfObservations)
106end
107
108assignin('base', 'mYY', Y'*Y);
109assignin('base', 'mYX', Y'*X);
110assignin('base', 'mXY', X'*Y);
111assignin('base', 'mXX', X'*X);
112assignin('base', 'Ydata', Y);
113assignin('base', 'Xdata', X);