This workbook is based upon the content of the RATS e-course on ARCH/GARCH and Volatility Models, offered in Fall 2012. Over the years, GARCH models have probably been the second most common application of the RATS software to appear in published articles (after Vector Autoregressions). Roughly half the course concerns the use of the existing GARCH instruction—determining the best specification, handling the estimation and doing tests of the adequacy of the model. The second half examines various extensions to the GARCH framework that require either more general likelihood maximization (Chapters 7 and 8), simulation methods (Chapters 9 and 10), or both, with detailed discussions of replications of papers which have been popular downloads by RATS users. The final chapter covers Stochastic Volatility Models, which are similar to GARCH but more complicated technically.

The second edition adds over 50 pages. Some changes reflect improvements to the GARCH instruction over the last few years, such as the new STDRESIDS and FACTORBY options for doing multivariate standardized residuals, and the new DENSITY and PARMSET options for using non-standard densities.

In addition, there is new or expanded coverage of

- ARMA models for the mean
- evaluating GARCH variance forecasts
- variance shift dummies derived from ICSS
- use/abuse of "rolling window" estimates
- generation of VECH representations for BEKK models
- tests for spillover in the mean and in the variance
- DCC models
- Variance Impulse Response Functions both closed form (for models that allow them) or through simulations (for models that don't)
- methods for handling extreme outliers
- GARCH-X models, particularly as they apply to BEKK
- VECM-GARCH models
- computing and displaying time-varying hedge ratios and portfolio weights
- Cermeño-Grier-style "panel GARCH" models

(358 pages, 37 examples)

1.2 Tips and Tricks

2.2 Extending to Multiple Series

2.3 Creating a Table

2.4 Tips and Tricks

3.2 The Example

3.3 Choosing the Mean Model

3.4 Testing for ARCH Effects

3.5 Maximum Likelihood Estimation with Gaussian errors

3.6 Diagnostics for univariate ARCH models

3.7 Maximum Likelihood Estimation with Non-Gaussian Errors

3.8 QMLE Estimation

3.9 GARCH Models

4.1.1 Evaluating Variance Forecasts

4.2 Stationarity

4.3 Stability Tests

4.4 Variance Equation Dummies

4.5 GARCH-M

4.6 Alternative Variance Models

4.7 Asymmetry

4.8 Rolling Samples

5.2 GARCH Instruction

5.3 Diagnostics

5.4 VECH, DVECH and BEKK Models

5.4.1 Diagonal VECH (Standard) Model

5.4.2 BEKK Model

5.5 Spillover

5.6 CC Models: Constant Correlation

5.7 DCC Models: Dynamic Conditional Correlation

5.8 RATS Tips and Tricks

5.8.1 Graphics with Multiple Series

5.8.2 Fancy Table of Diagnostics

6.2 Volatility Impulse Response Functions

6.2.1 Extensions of VIRF

6.3 Asymmetry

6.4 GARCH-X

6.5 Cointegrated Variables

6.6 Hedge Ratios and Related Calculations

7.2 GMM Estimation

7.3 GARCH Model with Multiplicative Factor

8.2 Panel GARCH

8.3 Non-standard Density

8.4 Structural VAR with GARCH

9.2 Value-at-risk (VaR) Calculations-Univariate

9.3 Value-at-risk (VaR) Calculations-Multivariate

9.4 Variance Impulse Responses by Simulation

9.5 RATS Tips and Tricks

10.2 Monte Carlo Methods

10.2.1 Importance Sampling

10.2.2 Markov Chain Monte Carlo

10.2.3 MCMC Estimation of DCC Correlations

10.3 RATS Tips and Tricks

11.2 Impulse Responses in an SVAR-GARCH-M Model

11.2.1 Error Bands

12.2 Gibbs Sampling

A.2 Univariate Student t

A.3 Gamma Distribution

A.4 Inverse Gamma Distribution

A.5 (Scaled) Inverse Chi-Squared Distribution

A.6 Multivariate Normal

A.7 Multivariate Student (t)

A.8 GED distribution