Citation:
[Journal:] Journal of Time Series Analysis [ISSN:] 1467-9892 [Volume:] 43 [Issue:] 5 [Publisher:] John Wiley & Sons, Ltd [Place:] Oxford, UK [Year:] 2022 [Pages:] 750-780
Publisher:
John Wiley & Sons, Ltd, Oxford, UK
Abstract:
We consider multivariate stationary processes (Xt) satisfying a stochastic recurrence equation of the form Xt=đtXtâ1+Qt, where (Qt) are i.i.d. random vectors and đt=Diag(b1+c1Mt,âŚ,bd+cdMt) are i.i.d. diagonal matrices and (Mt) are i.i.d. random variables. We obtain a full characterization of the vector scaling regular variation properties of (Xt), proving that some coordinates Xt,âi and Xt,âj are asymptotically independent even though all coordinates rely on the same random input (Mt). We prove the asynchrony of extreme clusters among marginals with different tail indices. Our results are applied to some multivariate autoregressive conditional heteroskedastic (BEKKâARCH and CCCâGARCH) processes and to logâreturns. Angular measure inference shows evidences of asymptotic independence among marginals of diagonal SRE with different tail indices.