# GARCH Models

## Estimating, simulating, and forecasting with GARCH models

GARCH models are conditionally heteroskedastic models with a constant unconditional variance. They have been widely used in financial and econometric modeling and analysis since the 1980s. These models are characterized by their ability to capture volatility clustering, and they are widely used to account for nonuniform variance in time-series data.

Effective approaches to modeling and analyzing univariate GARCH processes include:

• Estimating parameters of a univariate GARCH(p, q) model with Gaussian innovations
• Simulating univariate GARCH(p, q) processes
• Forecasting conditional variances

Additional time-series capabilities to consider for modeling stochastic processes include:

• Univariate ARMAX/GARCH composite models
• Multivariate VARMAX models
• Cointegration analysis

• estimate: Estimate ARMAX/GARCH Model Parameters - Function
• simulate: Simulate ARMAX/GARCH Model Responses - Function
• garch: Simulate Univariate GARCH Processes - Function