stepan-a / state-space-model-with-observed-exogenous-variables

Dynare example.

Provides an example of State Space Model with observed exogenous variables. The data generating process is as follows:

$$\begin{cases} y_t &= x_t + \beta_y v_t\\\ x_t &= \alpha x_{t-1} + \beta_x u_t + \varepsilon_t \end{cases}$$

where initial condition for the state variable is assumed to be deterministic, $x_{0} = 0$, the structural error $\varepsilon_{t}$ is a Gaussian white noise with mean 0 and variance $\sigma_{\varepsilon}^2$, $\alpha$ is real parameter with abolute value less than one, $\beta_y$ and $\beta_x$ are non zero real parameters, finally $\{u_t\}$ and $\{v_t\}$ are exogenous stochastic processes.

Datasets are generated by dgp/simulexogenousvariables.mod and dgp/simulsample.m. Data can be obtained using the Makefile in the dgp folder:

~$ make all

the data are saved in file data/sample.mat which can be used to instantiate a dseries object. The mod files under subfolder estim/ provide estimates of the State Space Model.