2015/05/20 by Muneya Matsui, Thomas Mikosch, Matsui, Muneya +1
Mathematics · #62M10 #91B84 #FOS: Mathematics #Primary 60G70 #Probability (math.PR) #Secondary 60G10 #Statistics Theory (math.ST) #math.PR #math.ST #msc:60G10 #msc:60G70 #msc:62M10 #msc:91B84 #stat.TH
paper · pdf · doi:10.48550/arxiv.1505.05385
21 pages, 31 figures,
arxiv created 2015/05/20 · arxiv updated 2015/05/21
In this paper, we derive some asymptotic theory for the extremogram and cross-extremogram of a bivariate GARCH(1,1) process. We show that the tails of the components of a bivariate GARCH(1,1) process may exhibit power law behavior but, depending on the choice of the parameters, the tail indices of the components may differ. We apply the theory to 5-minute return data of stock prices and foreign exchange rates. We judge the fit of a bivariate GARCH(1,1) model by considering the sample extremogram and cross-extremogram of the residuals. The results are in agreement with the iid hypothesis of the two-dimensional innovations sequence. The cross-extremograms at lag zero have a value significantly distinct from zero. This fact points at some strong extremal dependence of the components of the innovations.