# Standard State-Space Model

States have 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, see What Are State-Space Models?.

## Functions

expand all

 `ssm` Create state-space model
 `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
 `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
 `irf` Impulse response function (IRF) of state-space model `irfplot` Plot impulse response function (IRF) of state-space model `fevd` Generate forecast error variance decomposition (FEVD) of state-space model `corr` Model-implied temporal correlations of state-space model
 `simulate` Monte Carlo simulation of state-space models `simsmooth` State-space model simulation smoother
 `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.

What Are State-Space Models?

Learn state-space model definitions and how to create a state-space model object.

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  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.

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.

### 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.

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.