Asymptotic independence ex machina: Extreme value theory for the diagonal SRE model

Abstract

We consider multivariate stationary processes (X t ) satisfying a stochastic recurrence equation of the formwhere (Q t ) are iid random vectors andare iid diagonal matrices and (M t ) are iid random variables. We obtain a full characterization of the Vector Scaling Regular Variation properties of (X t ), proving that some coordinates X t,i and X t,j are asymptotically independent even though all coordinates rely on the same random input (M t ). We prove the asynchrony of extreme clusters among marginals with different tail indices. Our results are applied to some multivariate autoregressive conditional heteroskedastic (BEKK-ARCH and CCC-GARCH) processes and to log-returns. Angular measure inference shows evidences of asymptotic independence among marginals of diagonal SRE with different tail indices.