A Multivariate GARCH Model Incorporating the Direct and Indirect Transmission of Shocks

The risks associated with exchange rate and money market indicators have drawn the attentions of econometricians, researchers, statisticians, and even investors in deposit money banks in Nigeria. The study targeted at modeling exchange rate and Nigerian deposit banks money market dynamics using trivariate form of multivariate GARCH model. Data for the period spanning from 1991 to 2017 on exchange rate (Naira/Dollar) and money market indicators (Maximum and prime lending rate) were sourced for from the central bank of Nigeria (CBN) online statistical database. The study specifically investigated; the dynamics of the variance and covariance of volatility returns between exchange rate and money market indicators in Nigeria were examine whether there exist a linkage in terms of returns and volatility transmission between exchange rate and money market indicators in Nigeria and compared the difference in Multivariate BEKK GARCH considering restrictive indefinite under the assumption of normality and that of student’s –t error distribution. Preliminary time series checks were done on the data and the results revealed the present of volatility clustering. Results reveal the estimate of the maximum lag for exchange rate and money market indicators were 4 respectively. Also, the results confirmed that there were two co-integrating equations in the relationship between the returns on exchange rate and money market indicators. The results of the diagonal MGARCH –BEKK estimation confirmed that diagonal MGARCH –BEKK in students’-t was the best fitted and an appropriate model for modeling exchange rate and Nigerian deposit money market dynamics using trivariate form of multivariate GARCH model. Also, the study confirmed presence of two directional volatility spillovers between the two sets of variables.

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Detecting Shocks in The Economic Development Dynamics of Selected Countries

Folia Oeconomica Stetinensia ◽

10.2478/foli-2013-0018 ◽

2014 ◽

Vol 13 (2) ◽

pp. 120-133

Author(s):

Anna Janiga-Ćmiel

Keyword(s):

Estimation Method ◽

Garch Model ◽

Positive Definite ◽

Multivariate Garch ◽

Contagion Effect ◽

Multivariate Models ◽

The United Kingdom ◽

Multivariate Garch Model ◽

Polish Economy ◽

The Impact

Abstract The paper examines the development of the Polish economy as well as the economies of selected countries in the period from 2001 to 2012. For that purpose, models based on the GDP growth in particular countries were built. A comparative analysis of the development of economies in the countries concerned (the United Kingdom, Belgium, Denmark, France, Poland, the Netherlands), based on a specially built full-factor multivariate GARCH model, is presented. The theory of the construction of a full-factor multivariate GARCH model and its estimation method are discussed. In the paper, a multivariate GARCH model where the covariance matrix is always positive, deﬁnite and the number of parameters is relatively small compared to other multivariate models is proposed. The causality of the impact that economies exert on one another is examined and the occurrence of the contagion effect is verified by means of the Forbes and Rigobon test.

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Copula multivariate GARCH model with constrained Hamiltonian Monte Carlo

Dependence Modeling ◽

10.1515/demo-2019-0006 ◽

2019 ◽

Vol 7 (1) ◽

pp. 133-149

Author(s):

Martin Burda ◽

Louis Bélisle

Keyword(s):

Monte Carlo ◽

Garch Model ◽

Tail Dependence ◽

Copula Function ◽

Multivariate Garch ◽

Hamiltonian Monte Carlo ◽

Dynamic Copula ◽

Multivariate Garch Model ◽

Financial Asset Returns ◽

Parameter Constraints

AbstractThe Copula Multivariate GARCH (CMGARCH) model is based on a dynamic copula function with time-varying parameters. It is particularly suited for modelling dynamic dependence of non-elliptically distributed financial returns series. The model allows for capturing more flexible dependence patterns than a multivariate GARCH model and also generalizes static copula dependence models. Nonetheless, the model is subject to a number of parameter constraints that ensure positivity of variances and covariance stationarity of the modeled stochastic processes. As such, the resulting distribution of parameters of interest is highly irregular, characterized by skewness, asymmetry, and truncation, hindering the applicability and accuracy of asymptotic inference. In this paper, we propose Bayesian analysis of the CMGARCH model based on Constrained Hamiltonian Monte Carlo (CHMC), which has been shown in other contexts to yield efficient inference on complicated constrained dependence structures. In the CMGARCH context, we contrast CHMC with traditional random-walk sampling used in the previous literature and highlight the benefits of CHMC for applied researchers. We estimate the posterior mean, median and Bayesian confidence intervals for the coefficients of tail dependence. The analysis is performed in an application to a recent portfolio of S&P500 financial asset returns.

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