www.gusucode.com > econ 案例源码程序 matlab代码 > econ/ConvertVARModelToVECModelUsingCellArrayExample.m
%% Convert VAR Model to VEC Model Using Cell Arrays % Consider converting the following VAR(3) model to a VEC(2) model. % % $${y_t} = \left[ {\begin{array}{*{20}{c}} % {0.5}\\ % {1}\\ % { - 2} % \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} % {0.54}&{0.86}&{ - 0.43}\\ % {1.83}&{0.32}&{0.34}\\ % { - 2.26}&{ - 1.31}&{3.58} % \end{array}} \right]{y_{t - 1}} + \left[ {\begin{array}{*{20}{c}} % {0.14}&{ - 0.12}&{0.05}\\ % {0.14}&{0.07}&{0.10}\\ % {0.07}&{0.16}&{0.07} % \end{array}} \right]{y_{t - 3}} + {\varepsilon _t}.$$ % %% % Specify the coefficient matrices ($A_1$, $A_2$, and $A_3$) of the VAR(3) % model terms $y_{t-1}$, $y_{t-2}$, and $y_{t-3}$. % Copyright 2015 The MathWorks, Inc. A1 = [0.54 0.86 -0.43; 1.83 0.32 0.34; -2.26 -1.31 3.58]; A2 = zeros(3); A3 = [0.14 -0.12 0.05; 0.14 0.07 0.10; 0.07 0.16 0.07]; %% % Pack the matrices into separate cells of a 3 dimensional cell vector. Put |A1| % into the first cell, |A2| into the second cell, and |A3| into the third % cell. VAR = {A1 A2 A3}; %% % Compute the coefficient matrices of $\Delta y_{t-1}$ and $\Delta % y_{t-2}$, and error-correction coefficient matrix of the equivalent % VEC(2) model. [VEC,C] = var2vec(VAR); size(VEC) %% % The specification of a cell array of matrices for the input argument % indicates that the VAR(3) model is a reduced-form model expressed as a % difference equation. |VAR{1}| is the coefficient of $y_{t-1}$, and % subsequent elements correspond to subsequent lags. %% % |VEC| is a 1-by-2 cell vector of 3-by-3 coefficient matrices for the % VEC(2) equivalent of the VAR(3) model. Because the VAR(3) model is in % reduced form, the equivalent VEC model is also. That is, |VEC{1}| is the % coefficient of $\Delta y_{t-1}$, and subsequent elements correspond to % subsequent lags. The orientation of |VEC| corresponds to the orientation % of |VAR|. %% % Display the VEC(2) model coefficients. B1 = VEC{1} B2 = VEC{2} C %% % Since the constant offsets between the models are equivalent, the % resulting VEC(2) model is % % $$\begin{array}{rcl}\Delta {y_t} &=& \left[ {\begin{array}{*{20}{c}} % {0.5}\\ % {1}\\ % { - 2} % \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} % { - 0.14}&{0.12}&{ - 0.05}\\ % { - 0.14}&{ - 0.07}&{ - 0.10}\\ % { - 0.07}&{ - 0.16}&{ - 0.07} % \end{array}} \right]\Delta {y_{t - 1}} + \left[ {\begin{array}{*{20}{c}} % { - 0.14}&{0.12}&{ - 0.05}\\ % { - 0.14}&{ - 0.07}&{ - 0.10}\\ % { - 0.07}&{ - 0.16}&{ - 0.07} % \end{array}} \right]\Delta {y_{t - 2}}\\ &+& \left[ {\begin{array}{*{20}{c}} % { - 0.32}&{0.74}&{ - 0.38}\\ % {1.97}&{ - 0.61}&{0.44}\\ % { - 2.19}&{ - 1.15}&{2.65} % \end{array}} \right]{y_{t - 1}} + {\varepsilon _t}\end{array}.$$ %