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## Create State-Space Model with Random State Coefficient

This example shows how to create a time-varying, state-space model containing a random, state coefficient.

Write a function that specifies how the parameters in `params` map to the state-space model matrices, the initial state values, and the type of state. Symbolically, the model is

` ` is a random coefficient.

``` % Copyright 2015 The MathWorks, Inc. function [A,B,C,D] = randomCoeffParamMap(c) % State-space model parameter-to-matrix mapping function with a random % coefficient example. There are two states: one is a random walk with % disturbance variance 1, and the other is a first-order Markov model with % a random coefficient and an unknown variance. The observation equation % is the sum of the two states, and the innovation has variance 1. A = diag([1,c(1)*rand]); B = [1 0; 0 c(2)]; C = [1,1]; D = 1; end ```

Create the state-space model by passing `randomCoeffParamMap` as a function handle to `ssm`.

```rng('default'); % For reproducibility Mdl = ssm(@randomCoeffParamMap); ```

`ssm` implicitly creates the `ssm` model `Mdl`.

Display `Mdl` using `disp`. Specify initial parameters values.

```disp(Mdl,[3; 5]) ```
```State-space model type: <a href="matlab: doc ssm">ssm</a> State vector length: 2 Observation vector length: 1 State disturbance vector length: 2 Observation innovation vector length: 1 Sample size supported by model: Unlimited State variables: x1, x2,... State disturbances: u1, u2,... Observation series: y1, y2,... Observation innovations: e1, e2,... State equations: x1(t) = x1(t-1) + u1(t) x2(t) = (0.38)x2(t-1) + (5)u2(t) Observation equation: y1(t) = x1(t) + x2(t) + e1(t) Initial state distribution: Initial state means x1 x2 0 0 Initial state covariance matrix x1 x2 x1 1e+07 0 x2 0 1e+07 State types x1 x2 Diffuse Diffuse ```

`disp` sets the parameters to their initial values, or functions of their initial values. In this case, the first parameter is the initial values times a random number.