# Standard State-Space Model

States with finite initial state variances

The standard state-space model implements the standard Kalman filter
and initial state variances of are finite. You can create a standard
state-space model by calling `ssm`

.

For an overview of supported state-space model forms and to learn how
to create a model in MATLAB^{®}, see Create Continuous State-Space Models for Economic Data Analysis.

## Functions

## Topics

### Create Model

**Explicitly Create State-Space Model Containing Known Parameter Values**

Create a time-invariant, state-space model containing known parameter values.**Create State-Space Model with Unknown Parameters**

Explicitly and implicitly create state-space models with unknown parameters.**Create State-Space Model Containing ARMA State**

Create a stationary ARMA model subject to measurement error.**Implicitly Create State-Space Model Containing Regression Component**

Create a state-space model that contains a regression component in the observation equation using a parameter-mapping function describing the model.**Create State-Space Model with Random State Coefficient**

Create a time-varying, state-space model containing a random, state coefficient.**Implicitly Create Time-Varying State-Space Model**

Create a time-varying, state-space model using a parameter-mapping function describing the model.**Create Continuous State-Space Models for Economic Data Analysis**

Learn how Econometrics Toolbox™ supports state-space modeling of time series.**What Is the Kalman Filter?**

Learn about the Kalman filter, and associated definitions and notations.

### Fit Model to Data

**Estimate Time-Invariant State-Space Model**

Generate data from a known model, specify a state-space model containing unknown parameters corresponding to the data generating process, and then fit the state-space model to the data.**Estimate Time-Varying State-Space Model**

Fit time-varying state-space model to data.**Estimate State-Space Model Containing Regression Component**

Fit a state-space model that has an observation-equation regression component.**Estimate Random Parameter of State-Space Model**

Estimate a random, autoregressive coefficient of a state in a state-space model.**Assess State-Space Model Stability Using Rolling Window Analysis**

Check whether state-space model is time varying with respect to parameters.**Apply State-Space Methodology to Analyze Diebold-Li Yield Curve Model**

This example shows how to use state-space models (SSM) and the Kalman filter to analyze the Diebold-Li*yields-only and yields-macro models*[2] of monthly yield-curve time series derived from U.S.**Rolling-Window Analysis of Time-Series Models**

Estimate explicitly and implicitly defined state-space models using a rolling window.

### Estimate State Variables

**Filter States of State-Space Model**

Filter states of a known, time-invariant, state-space model.**Smooth States of State-Space Model**

Smooth the states of a known, time-invariant, state-space model.**Filter Data Through State-Space Model in Real Time**

This example shows how to*nowcast*a state-space model.**Filter Time-Varying State-Space Model**

Generate data from a known model, fit a state-space model to the data, and then filter the states.**Smooth Time-Varying State-Space Model**

Generate data from a known model, fit a state-space model to the data, and then smooth the states.**Compare Hodrick-Prescott Filter Formulations**

Compare two formulations of the Hodrick-Prescott filter: the closed-form solution of the programming problem and its state-space formulation, with a focus on how each formulation addresses missing observations.**Filter States of State-Space Model Containing Regression Component**

Filter states of a time-invariant, state-space model that contains a regression component.**Smooth States of State-Space Model Containing Regression Component**

Smooth states of a time-invariant, state-space model that contains a regression component.

### Characterize Dynamic Behavior

**Analyze Linearized DSGE Models**

Analyze a dynamic stochastic general equilibrium (DSGE) model using Bayesian state-space model tools.

### Generate Monte Carlo Simulations

**Simulate States and Observations of Time-Invariant State-Space Model**

Simulate states and observations of a known, time-invariant state-space model.**Simulate Time-Varying State-Space Model**

Generate data from a known model, fit a state-space model to the data, and then simulate series from the fitted model.**Forecast State-Space Model Using Monte-Carlo Methods**

Forecast a state-space model using Monte-Carlo methods, and to compare the Monte-Carlo forecasts to the theoretical forecasts.**Simulate States of Time-Varying State-Space Model Using Simulation Smoother**

Generate data from a known model, fit a state-space model to the data, and then simulate series from the fitted model using the simulation smoother.**Compare Simulation Smoother to Smoothed States**

Demonstrate how the results of the state-space model simulation smoother compare to the smoothed states.

### Generate Minimum Mean Square Error Forecasts

**Forecast State-Space Model Observations**

Forecast observations of a known, time-invariant, state-space model.**Forecast Time-Varying State-Space Model**

Generate data from a known model, fit a state-space model to the data, and then forecast states and observations states from the fitted model.**Model Local Trends in Global Carbon Emissions**

Analyze time-varying local trends in carbon emissions data by building dynamic state-space models from series for coal, gas, and oil.**Forecast Observations of State-Space Model Containing Regression Component**

Estimate a regression model containing a regression component, and then forecast observations from the fitted model.**Forecast State-Space Model Containing Regime Change in the Forecast Horizon**

Forecast a time-varying, state-space model, in which there is a regime change in the forecast horizon.**Choose State-Space Model Specification Using Backtesting**

Choose the state-space model specification with the best predictive performance using a rolling window.