On the Tail Behavior of a Class of Multivariate Conditionally Heteroskedastic Processes

Pedersen, Rasmus Søndergaard; Wintenberger, Olivier

doi:10.2139/ssrn.2900201

Cited by 8 publications

(35 citation statements)

References 40 publications

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“…The diagonal SRE (1.1) is a very simple model that may coincide with some classical multivariate GARCH ones. For the specific case (M t ) are iid N (0, 1), b i = 0 for all 1 ≤ i ≤ d and (Q t ) are iid N (0, Σ) the diagonal SRE coincides with the diagonal BEKK-ARCH(1) model as in [24]. For (Q t ) degenerated to a constant the diagonal SRE model coincides with the volatility process of some CCC-GARCH model.…”

Section: Introductionmentioning

confidence: 89%

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: Introductionmentioning

confidence: 89%

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

Mentemeier

Wintenberger

2022

Journal Time Series Analysis

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“…Note that we have more applications in GARCH-type models. Indeed, we are considering applications in BEKK-ARCH models, of which tail behavior has been investigated with the diagonal setting (see [25]). At there, we should widen our results into the case where the corresponding SRE takes values on whole real line.…”

Section: Applicationsmentioning

confidence: 99%

Tail indices for $$\mathbf{A}\mathbf{X}+\mathbf{B}$$ Recursion with Triangular Matrices

Matsui

Świątkowski

2020

J Theor Probab

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We study multivariate stochastic recurrence equations (SREs) with triangular matrices. If coefficient matrices of SREs have strictly positive entries, the classical Kesten result says that the stationary solution is regularly varying and the tail indices are the same in all directions. This framework, however, is too restrictive for applications. In order to widen applicability of SREs, we consider SREs with triangular matrices and we prove that their stationary solutions are regularly varying with component-wise different tail exponents. Several applications to GARCH models are suggested.

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“…The stationary component, ξ t , exhibits heavy-tailed behavior since it satisfies a stochastic recurrence equation. Pedersen and Wintenberger (2018) have recently considered the tail properties of processes of the form (2) for a more general specification of the random coefficient, Φ t , that includes BEKK-ARCH and DAR-type processes as special cases. It should be possible to show that the stationary distribution of ξ t as defined in (2)-(3) also has power-law tails under suitable conditions.…”

Section: The Unobserved Componentsmentioning

confidence: 99%

The Stochastic Stationary Root Model

Hetland

2018

Econometrics

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We propose and study the stochastic stationary root model. The model resembles the cointegrated VAR model but is novel in that: (i) the stationary relations follow a random coefficient autoregressive process, i.e., exhibhits heavy-tailed dynamics, and (ii) the system is observed with measurement error. Unlike the cointegrated VAR model, estimation and inference for the SSR model is complicated by a lack of closed-form expressions for the likelihood function and its derivatives. To overcome this, we introduce particle filter-based approximations of the log-likelihood function, sample score, and observed Information matrix. These enable us to approximate the ML estimator via stochastic approximation and to conduct inference via the approximated observed Information matrix. We conjecture the asymptotic properties of the ML estimator and conduct a simulation study to investigate the validity of the conjecture. Model diagnostics to assess model fit are considered. Finally, we present an empirical application to the 10-year government bond rates in Germany and Greece during the period from January 1999 to February 2018.

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On the Tail Behavior of a Class of Multivariate Conditionally Heteroskedastic Processes

Cited by 8 publications

References 40 publications

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

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

Tail indices for $$\mathbf{A}\mathbf{X}+\mathbf{B}$$ Recursion with Triangular Matrices

The Stochastic Stationary Root Model

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