Diagonal stochastic recurrence equation -- multivariate regular variation

Damek, Ewa

doi:10.48550/arxiv.2106.11243

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Ccc-garch(11) Model1

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2022

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“…We conjecture asymptotic independence to be true for all choices of N t in the original CCC-GARCH(1,1) model, since the one we considered is the most dependent one. A recent preprint Damek (2021) gives a partial positive answer to this open question.…”

Section: Ccc-garch(11) Modelmentioning

confidence: 99%

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

Mentemeier

Wintenberger

2022

Journal Time Series Analysis

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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.

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Section: Ccc-garch(11) Modelmentioning

confidence: 99%