www.gusucode.com > econ 案例源码程序 matlab代码 > econ/ExplicitlySpecifyAStateSpaceModelUnknownParametersExample.m
%% Explicitly Create State-Space Model Containing Unknown Parameters % This example shows how to create a time-invariant, state-space model % containing unknown parameter values using |ssm|. %% % Define a state-space model containing two dependent MA(1) states, and % an additive-error observation model. Symbolically, the equation is % % $$\left[ % \begin{array}{*{20}{c}}x_{t,1}\\x_{t,2}\\x_{t,3}\\x_{t,4}\end{array} % \right] = \left[ % {\begin{array}{*{20}{c}}0&\theta_1&\lambda_1&0\\0&0&0&0\\0&0&0&\theta_3\\0&0&0&0\end{array}} % \right]\left[ \begin{array}{*{20}{c}}x_{t - 1,1}\\x_{t - % 1,2}\\x_{t - 1,3}\\x_{t - 1,4}\end{array}\right] + \left[ % \begin{array}{*{20}{c}}{\sigma_1} & 0\\1 & 0 \\0 &\sigma_2\\ % 0&1\end{array} \right]\left[ % \begin{array}{*{20}{c}}u_{t,1}\\u_{t,2}\end{array} \right]$$ % % $${y_t} = \left[\begin{array}{*{20}{c}}1& 0 & 0 & 0\\0&0&1&0\end{array} % \right]\left[ % \begin{array}{*{20}{c}}x_{t,1}\\x_{t,2}\\x_{t,3}\\x_{t,4}\end{array} % \right] + \left[ {\begin{array}{*{20}{c}}\sigma_3& 0\\ 0&\sigma_4\end{array}} % \right]\left[\begin{array}{*{20}{c}}\varepsilon_{t,1}\\\varepsilon_{t,2}\end{array}\right].$$ % % Note that the states $x_{t,1}$ and $x_{t,3}$ are the two dependent MA(1) % processes. The states $x_{t,2}$ and $x_{t,4}$ help construct the % lag-one, MA effects. For example, $x_{t,2}$ picks up the first disturbance % ($u_{t,1}$), and $x_{t,1}$ picks up $x_{t - 1,2} = u_{t - 1,1}$. In all, % $x_{t,1} = \lambda_1x_{t-1,3} + u_{t,1} + \theta_1u_{t-1,1}$, which is an % MA(1) with $x_{t-1,3}$ as an input. %% % Specify the state-transition coefficient matrix. Use |NaN| values to % indicate unknown parameters. % Copyright 2015 The MathWorks, Inc. A = [0 NaN NaN 0; 0 0 0 0; 0 0 0 NaN; 0 0 0 0]; %% % Specify the state-disturbance-loading coefficient matrix. B = [NaN 0; 1 0; 0 NaN; 0 1]; %% % Specify the measurement-sensitivity coefficient matrix. C = [1 0 0 0; 0 0 1 0]; %% % Specify the observation-innovation coefficient matrix. D = [NaN 0; 0 NaN]; %% % Use |ssm| to define the state-space model. Mdl = ssm(A,B,C,D) %% % |Mdl| is an |ssm| model containing unknown parameters. A detailed % summary of |Mdl| prints to the Command Window. It is good practice to % verify that the state and observations equations are correct. %% % Pass |Mdl| and data to |estimate| to estimate the unknown parameters.