# GAUSS State-Space Modeling (SSLIB)¶

## Description¶

This package provides tools for estimating and evaluating time-invariant state-space models. In addition to providing the tools for custom state space models, it provides pre-built functions for state-space modeling of:

• ARIMA packages

• SARIMA packages

## Installation¶

The GAUSS State Space library can be installed and updated directly in GAUSS using the GAUSS Package Manager. It requires a working copy of GAUSS 22+.

For more information on installing the GAUSS Package Manager please see our video blog, Installing the GAUSS Package Manager.

## Dependencies¶

This library requires the installation of the following GAUSS libraries:

## Usage¶

Estimating custom state-space models using the sslib library requires:

• Setting up the state-space representation

• Calling the estimation function ssFit()

See our complete guide to getting started with state-space estimation in GAUSS for a full example.

## Commands¶

### Estimating custom models¶

 ssFit() Estimates parameters of a state-space model using Kalman filtering and maximum likelihood estimation. ssIRF() Computes the impulse response functions based on the final estimated parameters. ssPredict() Computes in sample predictions or out-of-sample forecasts based on the final estimated parameters. ssKalmanSmooth() Performs the Rauch-Tung-Striebel backward recursion smoother for state variables and state covariances.

### Pre-built models¶

 ssARIMA() Estimates parameters of a state-space model ARIMA(p, d, q) model using Kalman filtering and maximum likelihood estimation. ssSARIMA() Estimates parameters of a state-space model SARIMA(p, d, q)(p_s, d_s, q_s) model using Kalman filtering and maximum likelihood estimation.

### Model evaluation¶

 ssgetAIC() Computes Akaike’s information criterion from loglikelihood. ssgetAICC() Computes the corrected Akaike’s information criterion from loglikelihood. ssgetBIC() Computes the Schwarz’ Bayesian information criterion from loglikelihood. ssgetHQIC() Computes the Hannan–Quinn information criterion from loglikelihood. ssHeteroskedasticityTest() Tests the null hypothesis of no heteroskedasticity by comparing the sum-of-squares of the first third of the sample to the sum-of-squares of last third of the sample. Analogous to a Goldfeld-Quandt test. ssJarqueBera() Performs the Jarque-Bera goodness-of-fit test on model residuals. ssLjungBox() Computes the Ljung-Box test for autocorrelation. ssSkewness() Computes the sample skewness. ssKurtosis() Compute the sample kurtosis.