States that have finite initial state variances

**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.

**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.

**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.

**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.

State-space model definition and usages

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.