GARCH Toolbox

Models for the Conditional Mean and Variance

The GARCH Toolbox allows a flexible model description of the conditional mean, using a general ARMAX form. ARMAX models encompass autoregressive (AR), moving average (MA), and regression (X) models, in any combination. Specifically, the toolbox allows a general ARMAX(R,M,Nx) form for the conditional mean

(2-8)

where X is an explanatory regression matrix in which each column is a time series and X(t,k) denotes the tth row and kth column.

The GARCH Toolbox models the conditional variance as a standard GARCH process with Gaussian innovations. It allows a general GARCH(P,Q) form with Gaussian innovations for the conditional variance

(2-9)

Note    This GARCH model is based on Bollerslev's original paper [4], and also includes Engle's original ARCH model [8] as a special case.

GARCH Toolbox Overview

Conventions and Clarifications