GARCH Models

Estimating, simulating, and forecasting with GARCH models

GARCH models, short for generalized autoregressive conditional heteroskedasticity models, 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.

You can use MATLAB and related computational finance toolboxes to perform basic GARCH estimation, simulation, and forecasting. Financial Toolbox lets you work with univariate GARCH processes. You can:

• Estimate parameters of a univariate GARCH(p, q) model with Gaussian innovations
• Simulate univariate GARCH(p, q) processes
• Forecast conditional variances

Econometrics Toolbox provides additional time-series capabilities that include univariate ARMAX/GARCH composite models with several GARCH variants, multivariate VARMAX models, and cointegration analysis.

Examples and How To

• Introduction to Econometrics Toolbox 6:26 (Video)
• Specifying Static Time Series Models (Example)
• Comparing GARCH Models (Example)
• Simulating with GARCH Processes (Example)
• Forecasting Using GARCH Predictions (Example)

Software Reference

• GARCH Models (Documentation)
• Estimate ARMAX/GARCH Model Parameters (Function)
• Simulate ARMAX/GARCH Model Responses (Function)
• Simulate Univariate GARCH Processes (Function)

See also: cointegration, time-series analysis