Estimate State-Space Time Series Models

Definition of State-Space Time Series Model

The discrete-time state-space model for a time series is given by the following equations:

$\begin{array}{l} x (k T + T) = A x (k T) + K e (k T) \\ y (k T) = C x (k T) + e (k T) \end{array}$

where T is the sample time and y(kT) is the output at time instant kT.

The time series structure corresponds to the general structure with empty B and D matrices.

For information about general discrete-time and continuous-time structures for state-space models, see What Are State-Space Models?.

Estimate State-Space Models at the Command Line

You can estimate single-output and multiple-output state-space models at the command line for time-domain data (iddata object).

The following table provides a brief description of each command. The resulting models are idss model objects. You can estimate either continuous-time, or discrete-time models using these commands.

Commands for Estimating State-Space Time Series Models

Command	Description
`n4sid`	Noniterative subspace method for estimating linear state-space models.
`ssest`	Estimates linear time series models using an iterative estimation method that minimizes the prediction error.