What is it about?
GO-GARCH processes are often used to model heavy-tailed (financial) data. Some issues arise, though, if our data presents different marginal tail indexes which may imply a good central fit but a poor fit to the extremes.
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Why is it important?
The possibility of modeling heavy tails using GARCH models has been rigorously established in the univariate case, and the consequences that this heavy tailedness has on the distributional limits of the sample autocovariance function are well known. In the multivariate case, however, the results are not fully developed or understood. We show that the sample autocovariance function for the GOGARCH process may either have a random limit or converge rather slowly to its population counterpart depending on how heavy the tails of the process are in accordance to the CCC-GARCH and the univariate GARCH cases.
Perspectives
The reader will find an analysis of both, the marginal and the finite--dimensional distributions of the GO-GARCH process. This analysis is used to explain the asymptotics of the sample ACF, a commonly used tool in TSA, and some alerts are risen which may impact how we use this tool. Also, the multivariate extremal distribution is layed out and clustering in extremes is shown to be a feature of the paths of the process. All these results translate what is well known for univariate GARCH processes into this multivariate version.
Dr Nelson O Muriel
Benemerita Universidad Autonoma de Puebla
Read the Original
This page is a summary of: A note on the tails of the GO-GARCH process, Stat, February 2014, Wiley,
DOI: 10.1002/sta4.41.
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