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Modeling the changing dependence of multivariate time series: with an application in financial econometrics

In this paper, we propose a new model for the multivariate time series, where the associations among the components are changing across time. The focus of the new model is to capture the extreme dependence phenomena that are common in financial econometrics. We propose using the α-VG distribution to capture the extreme dependence.  This α-VG distribution has three parameters: a shape parameter, a scale parameter and a tail parameter.  The tail parameter here is particularly designed to describe the tail heaviness of the distribution and will play an important role in modeling the extreme situation. Using this strategy, we have constructed several equations that model the changing dependence going with the updated information in a novel yet tractable manner.  In addition, the conditional normality of the new distribution has also brought great convenience to the carrying out statistical analysis with the new model. The relevant statistic issues associated with the proposed model are studied. The potential applications in the risk management in financial econometrics are discussed.