A Sufficient Condition for the Positive Definiteness of the Covariance Matrix of a Multivariate GARCH Model

2001 ◽  
Author(s):  
Gheorghe Silberberg ◽  
Szilard Pafka
Keyword(s):  
Covariance Matrix ◽  
Garch Model ◽  
Positive Definiteness ◽  
Multivariate Garch ◽  
Sufficient Condition ◽  
Multivariate Garch Model

A full-factor multivariate GARCH model

2003 ◽  
Vol 6 (2) ◽  
pp. 312-334 ◽  
Author(s):  
I. D. Vrontos ◽  
P. Dellaportas ◽  
D. N. Politis
Keyword(s):  
Garch Model ◽  
Multivariate Garch ◽  
Multivariate Garch Model

scholarly journals NEGATIVE VOLATILITY SPILLOVERS IN THE UNRESTRICTED ECCC-GARCH MODEL

2009 ◽  
Vol 26 (3) ◽  
pp. 838-862 ◽  
Author(s):  
Christian Conrad ◽  
Menelaos Karanasos
Keyword(s):  
Covariance Matrix ◽  
Garch Model ◽  
Positive Definiteness ◽  
Time Varying ◽  
Conditional Covariance ◽  
Conditional Correlation ◽  
Economic Theories ◽  
Model Builder ◽  
Volatility Spillovers ◽  
Volatility Feedback

This paper considers a formulation of the extended constant or time-varying conditional correlation GARCH model that allows for volatility feedback of either the positive or negative sign. In the previous literature, negative volatility spillovers were ruled out by the assumption that all the parameters of the model are nonnegative, which is a sufficient condition for ensuring the positive definiteness of the conditional covariance matrix. In order to allow for negative feedback, we show that the positive definiteness of the conditional covariance matrix can be guaranteed even if some of the parameters are negative. Thus, we extend the results of Nelson and Cao (1992) and Tsai and Chan (2008) to a multivariate setting. For the bivariate case of order one, we look into the consequences of adopting these less severe restrictions and find that the flexibility of the process is substantially increased. Our results are helpful for the model-builder, who can consider the unrestricted formulation as a tool for testing various economic theories.

scholarly journals Modeling Exchange Rate and Nigerian Deposit Money Market Dynamics Using Trivariate form of Multivariate GARCH Model

2019 ◽  
pp. 1-18
Author(s):  
Deebom, Zorle Dum ◽  
Tuaneh, Godwin Lebari
Keyword(s):  
Exchange Rate ◽  
Garch Model ◽  
Money Market ◽  
Multivariate Garch ◽  
Market Dynamics ◽  
Volatility Clustering ◽  
Volatility Spillovers ◽  
Multivariate Garch Model ◽  
The Difference ◽  
Student’S T

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.

scholarly journals Detecting Shocks in The Economic Development Dynamics of Selected Countries

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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