Extremal behavior of models with multivariate random recurrence representation.

For the solution Y of a multivariate random recurrence model Y_n = A_nY_n−1+ζ_n in R^q we investigate the extremal behaviour of the process y_n=z′_*Yn, nε N, for z_*ε R^q with |z| = 1. This extends results for positive matrices A_n. Moreover, we obtain explicit representations of the compound Poisson limit of point processes of exceedances over high thresholds in terms of its Poisson intensity and its jump distribution, which represents the cluster behaviour of such models on high levels. As a principal example we investigate a random coefficient autoregressive process.      «

For the solution Y of a multivariate random recurrence model Y_n = A_nY_n−1+ζ_n in R^q we investigate the extremal behaviour of the process y_n=z′_*Yn, nε N, for z_*ε R^q with |z| = 1. This extends results for positive matrices A_n. Moreover, we obtain explicit representations of the compound Poisson limit of point processes of exceedances over high thresholds in terms of its Poisson intensity and its jump distribution, which represents the cluster behaviour of such models on high levels. As a principal...     »