Multivariate GARCH Models (original) (raw)
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Multivariate GARCH models: a survey
Journal of applied …, 2006
This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications and inference methods, and identifies likely directions of future research. MULTIVARIATE GARCH MODELS 81
A full-factor multivariate GARCH model
Econometrics Journal, 2003
A new multivariate time series model with time varying conditional variances and covariances is presented and analysed. A complete analysis of the proposed model is presented consisting of parameter estimation, model selection and volatility prediction. Classical and Bayesian techniques are used for the estimation of the model parameters. It turns out that the construction of our proposed model allows easy maximum likelihood estimation and construction of well-mixing Markov chain Monte Carlo (MCMC) algorithms. Bayesian model selection is addressed using MCMC model composition. The problem of accounting for model uncertainty is considered using Bayesian model averaging. We provide implementation details and illustrations using daily rates of return on eight stocks of the US market.
In these notes we present a survey of the theory of univariate and multivariate GARCH models. ARCH, GARCH, EGARCH and other possible nonlinear extensions are examined. Conditions for stationarity (weak and strong) are presented. Inference and testing is presented in the quasi-maximum likelihood framework. Multivariate parameterizations are examined in details.
GARCH 101: An Introduction to the Use of ARCH/GARCH models in Applied Econometrics
2008
ARCH and GARCH models have become important tools in the analysis of time series data, particularly in financial applications. These models are especially useful when the goal of the study is to analyze and forecast volatility. This paper gives the motivation behind the simplest GARCH model and illustrates its usefulness in examining portfolio ris . Extensions are briefly discussed.
GO-GARCH: a multivariate generalized orthogonal GARCH model
IEEE Transactions on Knowledge and Data Engineering, 2002
Multivariate GARCH specifications are typically determined by means of practical considerations such as the ease of estimation, which often results in a serious loss of generality. A new type of multivariate GARCH model is proposed, in which potentially large covariance matrices can be parameterized with a fairly large degree of freedom while estimation of the parameters remains feasible. The model can be seen as a natural generalization of the O-GARCH model, while it is nested in the more general BEKK model. In order to avoid convergence difficulties of estimation algorithms, we propose to exploit unconditional information first, so that the number of parameters that need to be estimated by means of conditional information is more than halved. Both artificial and empirical examples are included to illustrate the model.
2007
In this paper we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new Double Smooth Transition Conditional Correlation GARCH model extends the Smooth Transition Conditional Correlation GARCH model of Silvennoinen and Teräsvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC–GARCH model, and another one to test for another transition in the STCC–GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. The model is applied to a selection of world stock indices, and it is found that time is an important factor affecting correlations between them.
Flexible multivariate GARCH modeling with an application to international stock markets
Review of Economics and Statistics, 2003
This paper offers a new approach to estimating time-varying covariance matrices in the framework of the diagonal-vech version of the multivariate GARCH(1,1) model. Our method is numerically feasible for large-scale problems, produces positive semide nite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator with a number of existing ones.
Abstract on GARCH Models: Financial modeling
Academia Letters, 2021
Until the early 1980s, econometrics developed at a relatively slow pace. It was very difficult to break free from the classical statistical paradigm. But with the meteoric rise of information technology, econometrics has experienced a significant increase in the past twenty years. Just think of the rampant proliferation of non-linear econometric models, volatility models and new estimation techniques like GMM or the simulated moment method, to name a few new fields in contemporary econometrics. But what is even more striking is the advancing pace of econometrics in the field of financial theory. Indeed, the theory of derivatives, which has its source in the early 1970s, increasingly uses econometric models of volatility, such as GARCH models, and the GMM method to estimate the parameters of stochastic differential equations, which are used to determine option prices, among others. Econometrics has also enabled the CAPM model, well known in financial theory, to overcome its static framework. We can now speak of timevarying betas and the transposition of the GARCH approach to CAPM has made it possible to situate it in a multivariate framework. On the other hand, modeling volatility is an important issue in research on the financial and energy markets. However, there is no answer for the choice of the best models and the measures of price volatility are due to the complexity of the energy price rebate where this problem motivated several researchers after the financial crisis of 2008. Relations between the stock market and the oil market have attracted particular attention from practitioners and academics. A strong relationship between them would have significant implications for political and economic decisions since negative shocks affecting one market can be quickly transmitted to the other through contagious effects. Empirical evidence on the relationship between stock and oil prices has been documented by numerous studies. Several works deal with the impact of the price of oil on stock market
Multivariate GARCH Models for the Greater China Stock Markets
2009
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