Abstract
We derive 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 five-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 crossextremogram of the residuals. The results are in agreement with the independent and identically distributed 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.
| Original language | English |
|---|---|
| Journal | Advances in Applied Probability |
| Volume | 48 |
| Issue number | A |
| Pages (from-to) | 217 - 233 |
| ISSN | 0001-8678 |
| DOIs | |
| Publication status | Published - 2016 |