# Diffuse State-Space Model

States can have infinite initial variances

The diffuse state-space model implements the diffuse Kalman filter and initial state variances of infinite. You can create a diffuse state-space model by calling `dssm`.

For an overview of supported state-space model forms, see What Are State-Space Models?.

## Functions

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 `dssm` Create diffuse state-space model
 `estimate` Maximum likelihood parameter estimation of diffuse state-space models `refine` Refine initial parameters to aid diffuse state-space model estimation `disp` Display summary information for diffuse state-space model
 `filter` Forward recursion of diffuse state-space models `smooth` Backward recursion of diffuse state-space models
 `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
 `forecast` Forecast states and observations of diffuse state-space models

## Topics

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.

Implicitly Create Time-Varying Diffuse State-Space Model

Create a diffuse state-space model in which one of the state variables drops out of the model after a certain period.

Implicitly Create Diffuse State-Space Model Containing Regression Component

Create a diffuse state-space model that contains a regression component in the observation equation using a parameter-mapping function describing the model.

Estimate Time-Varying Diffuse State-Space Model

Fit diffuse state-space model to data.

Filter Time-Varying Diffuse State-Space Model

Generate data from a known model, fit a diffuse state-space model to the data, and then filter the states.

Smooth Time-Varying Diffuse State-Space Model

Generate data from a known model, fit a diffuse state-space model to the data, and then smooth the states.

Forecast Time-Varying Diffuse State-Space Model

Generate data from a known model, fit a diffuse state-space model to the data, and then forecast states and observations states from the fitted model.