A continuous state-space Markov process, or state-space model, allows for trajectories through a continuous state space. The underlying Markov process is typically unobserved. A supplemental observation equation describes the evolution of measurable characteristics of the system, dependent on the Markov process. State-space models specify the structure of unobserved dynamic processes, and the composition of the processes into observations. Econometrics Toolbox™ state-space functionality accommodates time-invariant or time-varying linear state-space models containing mean-zero Gaussian state disturbances and observation innovations. The initial state distributions can be stationary, constant, or diffuse.
You can create a standard or diffuse state-space model using
dssm, respectively. After creating
a state-space model, you can estimate any unknown parameters using
time-series data, obtain filtered states, smooth states, generate forecasts,
or characterize its dynamic behavior. To filter and smooth states,
Econometrics Toolbox implements the standard or diffuse Kalman filter.
- Standard State-Space Model
States have finite initial state variances
- Diffuse State-Space Model
States can have infinite initial variances