GARCH Toolbox

Preface

Using This Guide

Related Products

Typographical Conventions

Introduction

What Is the GARCH Toolbox?

Software Requirements and Compatibility

Expected Background

Technical Conventions

Tutorial

GARCH Overview

Introducing GARCH

Using GARCH to Model Financial Time Series

GARCH Toolbox Overview

Models for the Conditional Mean and Variance

Conventions and Clarifications

The Default Model

Analysis and Estimation Example Using the Default Model

Pre-Estimation Analysis

Parameter Estimation

Post-Estimation Analysis

The GARCH Specification Structure

Purpose of the Specification Structure

Contents of the Specification Structure

Valid Model Specifications

Accessing Specification Structures

Using the Specification Structure for Estimation, Simulation, and Forecasting

Simulation

Simulating Sample Paths

Transients in the Simulation Process

A General Simulation Example

Forecasting

Computing a Forecast

Computing Root Mean Square Errors (RMSE)

Asymptotic Behavior for Long-Range Forecast Horizons

Conditional Mean Models with Regression Components

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

Model Selection and Analysis

Likelihood Ratio Tests

Akaike and Bayesian Information Criteria

Equality Constraints and Parameter Significance

Equality Constraints and Initial Parameter Estimates

Recommendations and Suggestions

Simplicity/Parsimony

Convergence Issues

Initial Parameter Estimates

Boundary Constraints and Statistical Inferences

Data Size and Quality

Function Reference

Functions - By Category

GARCH Modeling

GARCH Innovations Inference

Log-Likelihood Objective Functions

Statistics and Tests

GARCH Specification Structure Interface Functions

Helpers and Utilities

Graphics

Functions - Alphabetical List

Glossary

Bibliography

Index


 Preface