Asymptotic independence <i>ex machina</i> : Extreme value theory for the diagonal SRE model

We consider multivariate stationary processes ( X t ) satisfying a stochastic recurrence equation of the form = ???? ? 1 + Q , where are i.i.d. random vectors and Diag b c M … d diagonal matrices (Mt) variables. obtain full characterization vector scaling regular variation properties ), proving that some coordinates Xt, i j asymptotically independent even though all rely on same input (Mt). prove asynchrony extreme clusters among marginals with different tail indices. Our results applied to autoregressive conditional heteroskedastic (BEKK-ARCH CCC-GARCH) log-returns. Angular measure inference shows evidences asymptotic independence SRE