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

Create Model

ssm Create standard linear Gaussian state-space model

Fit Model to Data

`estimate`	Maximum likelihood parameter estimation of state-space models
`refine`	Refine initial parameters to aid state-space model estimation
`disp`	Display summary information for state-space model

Estimate State Variables

`filter`	Forward recursion of state-space models
`smooth`	Backward recursion of state-space models
`update`	Real-time state update by state-space model Kalman filtering (Since R2021b)

Characterize Dynamic Behavior

`irf`	Impulse response function (IRF) of state-space model (Since R2020b)
`irfplot`	Plot impulse response function (IRF) of state-space model (Since R2020b)
`fevd`	Generate forecast error variance decomposition (FEVD) of state-space model (Since R2021a)
`corr`	Model-implied temporal correlations of state-space model (Since R2021a)

Generate Monte Carlo Simulations

`simulate`	Monte Carlo simulation of state-space models
`simsmooth`	State-space model simulation smoother

Generate Minimum Mean Square Error Forecasts

forecast Forecast states and observations of state-space models

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.