Tutorial (GARCH Toolbox)

GARCH Toolbox

Using the Specification Structure for Estimation, Simulation, and Forecasting

The three functions, garchfit, garchpred, and garchsim, comprise the core analysis and modeling routines of the GARCH Toolbox. These three functions operate on the GARCH specification structure. Table 2-1, GARCH Specification Structure Use describes each function's use of the GARCH specification structure.

Table 2-1: GARCH Specification Structure Use
Function
Description
Use of GARCH Specification Structure

garchfit
Estimates the parameters of a conditional mean specification of ARMAX form and a conditional variance specification of GARCH form.

Input .   Optionally accepts a GARCH specification structure as input. If the structure contains the model orders but no coefficient vectors (C, AR, MA, Regress, K, ARCH, GARCH), garchfit uses maximum likelihood to estimate the coefficients for an ARMAX/GARCH model of the specified orders. If the structure contains coefficient vectors, garchfit uses them as initial estimates for further refinement. If you provide no specification structure, garchfit assumes, and returns, a specification structure for the default model.
Output.   Returns a specification structure that contains a fully specified ARMAX/GARCH model.

garchpred
Provides minimum-mean-square-error (MMSE) forecasts of the conditional mean and standard deviation of a return series, for a specified number of periods into the future.

Input.   Requires a GARCH specification structure that contains the coefficient vectors for the model for which garchpred is to forecast the conditional mean and standard deviation.
Output.   garchpred does not modify or return the specification structure.

garchsim
Uses Monte Carlo methods to simulates sample paths for return series, innovations, and conditional standard deviation processes.

Input.   Requires a GARCH specification structure that contains the coefficient vectors for the model for which garchsim is to simulate sample paths.
Output.   garchsim does not modify or return the specification structure.

Table 2-1: **GARCH Specification Structure Use**
Function	Description	Use of GARCH Specification Structure
`garchfit`	Estimates the parameters of a conditional mean specification of ARMAX form and a conditional variance specification of GARCH form.	Input . Optionally accepts a GARCH specification structure as input. If the structure contains the model orders but no coefficient vectors (`C`, `AR`, `MA`, `Regress`, `K`, `ARCH`, `GARCH`), `garchfit` uses maximum likelihood to estimate the coefficients for an ARMAX/GARCH model of the specified orders. If the structure contains coefficient vectors, `garchfit` uses them as initial estimates for further refinement. If you provide no specification structure, `garchfit` assumes, and returns, a specification structure for the default model. Output. Returns a specification structure that contains a fully specified ARMAX/GARCH model.
`garchpred`	Provides minimum-mean-square-error (MMSE) forecasts of the conditional mean and standard deviation of a return series, for a specified number of periods into the future.	Input. Requires a GARCH specification structure that contains the coefficient vectors for the model for which `garchpred` is to forecast the conditional mean and standard deviation. Output. `garchpred` does not modify or return the specification structure.
`garchsim`	Uses Monte Carlo methods to simulates sample paths for return series, innovations, and conditional standard deviation processes.	Input. Requires a GARCH specification structure that contains the coefficient vectors for the model for which `garchsim` is to simulate sample paths. Output. `garchsim` does not modify or return the specification structure.

Accessing Specification Structures Simulation