Standard State-Space Model
R2026bStates 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. - Nowcast Dynamic Factor Model of US Gross Domestic Product
This example shows how to nowcast economic variables, or predict them at the current or near future period, and to evaluate a nowcasting model for mixed frequency and jagged-edge economic data. - Nowcast Bayesian Dynamic Factor Model of US Gross Domestic Product
This example shows how to nowcast economic variables, or predict them at the current or near future period, and to evaluate a nowcasting model for mixed frequency and jagged-edge economic data.
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.
