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.
