www.gusucode.com > econ 案例源码程序 matlab代码 > econ/ExplicitlyCreateAndDisplayTimeVaryingDiffuseExample.m
%% Explicitly Create and Display Time-Varying Diffuse State-Space Model %% % From periods 1 through 50, the state model is a diffuse AR(2) and a % stationary MA(1) model, and the observation model is the sum of the two % states. From periods 51 through 100, the state model includes the first % AR(2) model only. Symbolically, the state-space model is, for periods 1 % through 50, % % $$\begin{array}{c}\left[ % {\begin{array}{*{20}{c}}{{x_{1t}}}\\{{x_{2t}}}\\{{x_{3t}}}\\{{x_{4t}}}\end{array}} % \right] = \left[ {\begin{array}{*{20}{c}}{{\phi _1}}&{{\phi % _2}}&0&0\\1&0&0&0\\0&0&0&\theta \\0&0&0&0\end{array}} \right]\left[ % {\begin{array}{*{20}{c}}{{x_{1,t - 1}}}\\{{x_{2,t - 1}}}\\{{x_{3,t - % 1}}}\\{{x_{4,t - 1}}}\end{array}} \right] + \left[ % {\begin{array}{*{20}{c}}{{\sigma % _1}}&0&0&0\\0&0&0&0\\0&0&1&{\rm{0}}\\0&0&1&0\end{array}} \right]\left[ % {\begin{array}{*{20}{c}}{{u_{1t}}}\\{{u_{2t}}}\\{{u_{3t}}}\\{{u_{4t}}}\end{array}} % \right]\\{y_t} = {a_1}\left( {{x_{1t}} + {x_{3t}}} \right) + {\sigma % _2}{\varepsilon _t}\end{array},$$ % % for period 51, % % $$\begin{array}{c} % \left[ {\begin{array}{*{20}{c}} % {{x_{1t}}}\\ % {{x_{2t}}} % \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} % {{\phi _1}}&{{\phi _2}}&0&0\\ % 1&0&0&0 % \end{array}} \right]\left[ {\begin{array}{*{20}{c}} % {{x_{1,t - 1}}}\\ % {{x_{2,t - 1}}}\\ % {{x_{3,t - 1}}}\\ % {{x_{4,t - 1}}} % \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} % {{\sigma _1}}&0&0&0\\ % 0&0&0&0 % \end{array}} \right]\left[ % {\begin{array}{*{20}{c}}{{u_{1t}}}\\{{u_{2t}}}\\{{u_{3t}}}\\{{u_{4t}}}\end{array}} % \right]\\ % {y_t} = {a_2}{x_{1t}} + {\sigma _3}{\varepsilon _t} % \end{array}$$ % % and for periods 52 through 100, % % $$\begin{array}{c} % \left[ {\begin{array}{*{20}{c}} % {{x_{1t}}}\\ % {{x_{2t}}} % \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} % {{\phi _1}}&{{\phi _2}}\\ % 1&0 % \end{array}} \right]\left[ {\begin{array}{*{20}{c}} % {{x_{1,t - 1}}}\\ % {{x_{2,t - 1}}} % \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} % {{\sigma _1}}&0\\ % 0&0 % \end{array}} \right]\left[ {\begin{array}{*{20}{c}} % {{u_{1t}}}\\ % {{u_{2t}}} % \end{array}} \right]\\ % {y_t} = {a_2}{x_{1t}} + {\sigma _3}{\varepsilon _t.} % \end{array}$$ % %% % Specify the state-transition coefficient matrix. A1 = {[NaN NaN 0 0; 1 0 0 0; 0 0 0 NaN; 0 0 0 0]}; A2 = {[NaN NaN 0 0; 1 0 0 0]}; A3 = {[NaN NaN; 1 0]}; A = [repmat(A1,50,1);A2;repmat(A3,49,1)]; %% % Specify the state-disturbance-loading coefficient matrix. B1 = {[NaN 0 0 0; 0 0 0 0; 0 0 1 0; 0 0 1 0]}; B2 = {[NaN 0 0 0; 0 0 0 0]}; B3 = {[NaN 0; 0 0]}; B = [repmat(B1,50,1);B2;repmat(B3,49,1)]; %% % Specify the measurement-sensitivity coefficient matrix. C1 = {[NaN 0 NaN 0]}; C3 = {[NaN 0]}; C = [repmat(C1,50,1);repmat(C3,50,1)]; %% % Specify the observation-disturbance coefficient matrix. D1 = {NaN}; D3 = {NaN}; D = [repmat(D1,50,1);repmat(D3,50,1)]; %% % Create the diffuse state-space model. Specify that the initial state % distributions are diffuse for the states composing the AR model and % stationary for those composing the MA model. StateType = [2; 2; 0; 0]; Mdl = dssm(A,B,C,D,'StateType',StateType); %% % |Mdl| is an |dssm| model object. %% % The model is large and contains a different set of parameters for each % period. The software displays state and observation equations for the % first 10 and last 10 periods. You can choose which periods to display % the equations for using the |'Period'| name-value pair argument. %% % Display the diffuse state-space model, and use |'Period'| display the state and % observation equations for the 50th, 51st, and 52nd periods. disp(Mdl,'Period',50) disp(Mdl,'Period',51) disp(Mdl,'Period',52) %% % The software attributes a different set of coefficients for each period. % You might experience numerical issues when you estimate such models. % To reuse parameters among groups of periods, consider creating a % parameter-to-matrix mapping function.