GARCH Toolbox

Conditional Mean Models with Regression Components

The GARCH Toolbox allows conditional mean models with regression components, i.e., of general ARMAX(R,M,Nx) form.

Conditional mean models with a regression component introduce additional complexity in the sense that the GARCH Toolbox has no way of knowing what the explanatory data represents or how it was generated. This is in contrast to ARMA models, which have an explicit forecasting mechanism and well-defined stationarity/invertibility requirements.

All the primary functions in the GARCH Toolbox (i.e., garchfit, garchinfer, garchpred, and garchsim) accept an optional regression matrix X, which represents X in the equation above. You must ensure that the regression matrix you provide is valid and you must:

• Collect and format the past history of explanatory data you include in X
• As needed, forecast X into the future to form XF

This section discusses:

• Incorporating a Regression Model in an Estimation
• Simulation and Inference Using a Regression Component
• Forecasting Using a Regression Component
• Regression in a Monte Carlo Framework

Asymptotic Behavior for Long-Range Forecast Horizons

Incorporating a Regression Model in an Estimation