Preface
Using This Guide
Related Products
Typographical Conventions
Introduction
GARCH Overview
Introducing GARCH
Why Use GARCH?
GARCH Limitations
The GARCH Toolbox
Software Requirements and Compatibility
Expected Background
Technical Conventions
Data Sets
DEM2GBP
NASDAQ
NYSE
Examples
GARCH Overview
Modeling of Financial Time Series
Characteristics of Financial Time Series
Correlation and Forecasting of Financial Time Series
Serial Dependence in Innovations
Conditional Mean and Variance Models
Conditional Mean Model
Conditional Variance Models
Comments on the Models
The Default Model
Primary Toolbox Functions
Analysis and Estimation Example Using the Default Model
Preestimation Analysis
Parameter Estimation
Postestimation Analysis
GARCH Specification Structure
Introduction
Equation Variables and Parameter Names
Conditional Mean Model
Conditional Variance Models
Examples of Specification Structures
Reading and Writing Specification Structures
Creating and Modifying a Specification Structure
Retrieving Specification Structure Values
Simulation
Simulating Sample Paths
Introduction
Simulating a Single Path
Simulating Multiple Paths
Presample Data
Automatically Generated Presample Data
User-Specified Presample Data
Estimation
Maximum Likelihood Estimation
Initial Parameter Estimates
User-Specified Initial Estimates
Automatically Generated Initial Estimates
Parameter Bounds
Presample Observations
User-Specified Presample Observations
Automatically Generated Presample Observations
Termination Criteria and Optimization Results
MaxIter and MaxFunEvals
TolCon, TolFun, and TolX
Convergence
Optimization Results
Constraint Violation Tolerance
Examples
Specifying Presample Data
Presample Data and Transient Effects
Alternative Technique for Estimating ARMA(R,M) Parameters
Active Lower Bound Constraint
Determining Convergence Status
Forecasting
Minimum Mean Square Error Forecasting
Conditional Standard Deviations of Future Innovations
Conditional Mean Forecasts of the Return Series
MMSE Volatility Forecasts of Returns
RMSE Associated with Conditional Mean Forecasts
Presample Observations
Asymptotic Behavior for Long-Range Forecast Horizons
Examples
Computing a Forecast
Volatility Forecasts over Multiple Periods
Computing a Forecast with Multiple Realizations
Regression Components in Conditional Mean Models
Introduction
Incorporating a Regression Model in an Estimation
Fitting a Model to a Simulated Return Series
Fitting a Regression Model to the Same Return Series
Simulation and Inference Using a Regression Component
Forecasting Using a Regression Component
Forecasted Explanatory Data
Generating Forecasted Explanatory Data
Ordinary Least Squares Regression
Regression in a Monte Carlo Framework
Model Selection and Analysis
Likelihood Ratio Tests
Akaike and Bayesian Information Criteria
Equality Constraints and Parameter Significance
The Specification Structure Fix Fields
The GARCH(2,1) Model as an Example
Equality Constraints and Initial Parameter Estimates
Complete Model Specification
Empty Fix Fields
Limiting Use of Equality Constraints
Simplicity and Parsimony
Advanced Example
Estimating the Model
Forecasting
Monte Carlo Simulation
Comparing Forecasts with Simulation Results
Functions - By Category
GARCH Modeling
GARCH Innovations Inference
Statistics and Tests
GARCH Specification Structure Interface Functions
Helpers and Utilities
Graphics
Functions - Alphabetical List
Glossary
Bibliography
Printable Documentation (PDF)
Product Page