# Standard State-Space Model

States have finite initial state variances

## 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
 `irf` Impulse response function (IRF) of state-space model `irfplot` Plot impulse response function (IRF) of state-space model
 `simulate` Monte Carlo simulation of state-space models `simsmooth` State-space model simulation smoother `irf` Impulse response function (IRF) of state-space model `irfplot` Plot impulse response function (IRF) of state-space model
 `forecast` Forecast states and observations of state-space models

## Examples and How To

### 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.

### 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.

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.

Estimate Time-Varying State-Space Model

Fit time-varying state-space model to data.

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.

Estimate State-Space Model Containing Regression Component

Fit a state-space model that has an observation-equation regression component.

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.

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.

Using the Kalman Filter to Estimate and Forecast the Diebold-Li Model

In the aftermath of the financial crisis of 2008, additional solvency regulations have been imposed on many financial firms, placing greater emphasis on the market valuation and accounting of liabilities.

### 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.

## Concepts

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.

Rolling-Window Analysis of Time-Series Models

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