%% Display State-Space Model and Initial Values
% Define a state-space model containing two independent, autoregressive states, and where the observations are the deterministic sum of the two states. Symbolically, the system of equations is
% \left[
% {\begin{array}{*{20}{c}}{{x_{t,1}}}\\{{x_{t,2}}}\end{array}} \right] =
% \left[ {\begin{array}{*{20}{c}}{{\phi _1}}&0\\0&{{\phi _2}}\end{array}}
% \right]\left[ {\begin{array}{*{20}{c}}{{x_{t - 1,1}}}\\{{x_{t -
% 1,2}}}\end{array}} \right] + \left[
% {\begin{array}{*{20}{c}}{\sigma_1} & 0\\0 & \sigma_2\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&1\end{array}}
% \right]\left[
% {\begin{array}{*{20}{c}}{{x_{t,1}}}\\{{x_{t,2}}}\end{array}}
% \right].
% Specify the state-transition matrix.

A = [NaN 0; 0 NaN];

%
% Specify the state-disturbance-loading matrix.

B = [NaN 0; 0 NaN];

%
% Specify the measurement-sensitivity matrix.

C = [1 1];

%
% Specify an empty matrix for the observation disturbance matrix.

D = [];

%
% Use ssm to define the state-space model. Specify the initial state means and covariance matrix to as unknown parameters. Specify that the states are stationary.

Mean0 = nan(2,1);
Cov0 = nan(2,2);
StateType = zeros(2,1);
Mdl = ssm(A,B,C,D,'Mean0',Mean0,'Cov0',Cov0,'StateType',StateType);

% Mdl is an ssm model containing unknown parameters.
%
% Use disp to display the state-space model. Specify initial values for the unknown parameters and the initial state means and covariance matrix as follows:
% \phi_{1,0} = \phi_{2,0} = 0.1.
% \sigma_{1,0} = \sigma_{2,0} = 0.2.
% x_{1,0} = 1 and x_{2,0} = 0.5.
% \Sigma_{x_{1,0},x_{2,0}} = I_2.

params = [0.1; 0.1; 0.2; 0.2; 1; 0.5; 1; 0; 0; 1];
disp(Mdl,params)

% Copyright 2012 The MathWorks, Inc.