This paper is a review to the GARCH family’s models. Since the seminal paper of Engle from 1982, much advancement has been made in understanding GARCH models and their multivariate extensions. In MGARCH models parsimonious models should be used to overcome the difficulty of estimating the VEC model ensuring MGARCH modeling is to provide a realistic and parsimonious specification of the variance matrix ensuring its positivity.
BEKK models are flexible but require too many parameters for multiple time series of more than four elements. BEKK models are much more parsimonious but very restrictive for the cross-dynamics. They are not suitable if volatility transmission is the object of interest, but they usually do a good job in representing the dynamics of variances and covariance. DCC models allow for different persistence between variances and correlations, but impose common persistence in the latter (although this may be relaxed) Student’s t distribution assumption is more proper under negative skewness and high kurtosis of return series.
Understanding and predicting the temporal dependence in the second-order moments of asset returns is important for many issues in financial econometrics. It is now widely accepted that financial volatilities move together over time across assets and markets. Recognizing this feature through a multivariate modeling framework leads to more relevant empirical models than working with separate univariate models. From a financial point of view, it opens the door to better decision tools in various areas, such as asset pricing, portfolio selection, option pricing, and hedging and risk management. Indeed, unlike at the beginning of the 1990s, several institutions have now developed the necessary skills to use the econometric theory in a financial perspective.
Table of Contents
1. Introduction
2. Objective
3. Literature Review
3.1 Theoretical Review GARCH Type Models
3.1.1 Univariate GARCH
3.1.2 Empirical Review of Univariate GARCH Models
3.2 Multivariate GARCH Models
3.2. 1 Models of Conditional Covariance Matrix
3.2.1.1 VEC–GARCH Model
3.2.1.2 BEKK–GARCH Model
3.3. Models of Conditional Correlation Matrix
3.3.1 CCC–GARCH Model
3.3.2 Dynamic Conditional Correlation Model
3.4 Estimation of GARCH Model
3.4.1 Maximum Likelihood
3.5 Diagnostics of GARCH Models
3.6 Forecasting Performance
3.8 Empirical Review of MGARCH models
3.9 Exchange rate Volatility
4. Summary and Conclusions
5. Reference
Objectives and Scope
This paper provides a comprehensive review of the GARCH model family, focusing on their application in modeling and predicting time-varying volatility and covariance in financial time series, particularly within the context of exchange rates.
- Theoretical examination of Univariate and Multivariate GARCH models.
- Empirical review of GARCH applications in financial market volatility analysis.
- Technical evaluation of model estimation, diagnostic checking, and forecasting performance.
- Analysis of volatility transmission and spillover effects between currency markets.
Excerpt from the Book
3.1 Theoretical Review GARCH Type Models
The GARCH family of models was developed primarily to account for the empirical regularities of a certain category of financial data speculative price data. In order to best understand the development of GARCH models we first need to take stock of the empirical features of speculative price data. The following are the most important “stylized facts” regarding such data:
1 Thick tails: The data seem to be leptokurtic with a large concentration of observations around the mean and have more outliers relative to the Normal distribution.
2 Volatility clustering: This is best described by Mandelbrot (1963), “.large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes
3 Bell-shaped symmetry: In general the distributions seem to be bell-shaped and symmetric.
4 Leverage effects: This relates to the tendency of stock returns to be negatively correlated with changes in return volatility.
5 Co-movements in volatilities: Black (1976) observed that “In general it seems fair to say that when stock volatilities change, they all tend to change in the same direction”. This indicates that common factors may explain temporal variation in conditional second moments and also the possibility of linkages or spillovers between markets.
Summary of Chapters
1. Introduction: Discusses the importance of modeling temporal dependence in financial asset returns and introduces GARCH models as tools for analyzing volatility.
2. Objective: Outlines the primary goals of the review, which include understanding theoretical aspects of GARCH models and empirically reviewing exchange rate volatility.
3. Literature Review: Provides an extensive theoretical and empirical overview of univariate and multivariate GARCH models, including their estimation, diagnostic testing, and forecasting applications.
4. Summary and Conclusions: Summarizes the key findings regarding the effectiveness of various GARCH models in capturing volatility dynamics and concludes that model performance varies significantly by specification.
5. Reference: Lists the academic literature and sources utilized throughout the review.
Keywords
MGARCH, VEC, BEKK, DCC, Volatility, Exchange Rate, GARCH, ARCH, Conditional Variance, Financial Econometrics, Time Series, Volatility Clustering, Leverage Effect, Forecasting, Maximum Likelihood
Frequently Asked Questions
What is the primary focus of this paper?
The paper serves as a review of the GARCH family of models, specifically evaluating their utility in modeling time-varying variance and covariance in financial time series.
What are the central topics covered?
The work covers theoretical frameworks of GARCH models, empirical reviews of exchange rate volatility, model estimation techniques, and diagnostic performance checks.
What is the main research goal?
The main objective is to understand flexible and parsimonious GARCH models theoretically and to empirically review their application to exchange rate volatility.
Which methodologies are discussed?
The paper discusses univariate and multivariate GARCH models, including VEC, BEKK, CCC, and DCC specifications, alongside estimation via Quasi Maximum Likelihood.
What does the main body address?
The main body examines the evolution of GARCH models, from univariate ARCH/GARCH to multivariate extensions, and analyzes their performance in modeling volatility transmission between currencies.
Which keywords best describe this study?
Key terms include MGARCH, VEC, BEKK, DCC, Volatility, Exchange Rate, and Conditional Variance.
What is the "curse of dimensionality" mentioned regarding VEC-GARCH?
It refers to the large number of parameters that must be estimated in a general VEC model, which becomes computationally burdensome even with a small number of variables.
Why is the Student’s t distribution often preferred over Normal distribution in these models?
It is preferred because financial return series often exhibit negative skewness and high kurtosis (fat tails), which the Normal distribution fails to adequately capture.
What is the significance of the findings by Innocent et al. (2016) regarding Rwandan currency?
The study found that return series of the studied currencies did not Granger-cause each other, but the BEKK model successfully identified volatility spillover and transmission effects.
- Quote paper
- Tekle Bobo (Author), 2020, Multivariate GARCH models. The time varying variance-covariance for the exchange rate, Munich, GRIN Verlag, https://www.grin.com/document/950200
