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

Autor:	Muneya Matsui, Witold Świątkowski
Rok vydání:	2020
Předmět:	Statistics and Probability Multivariate statistics General Mathematics Autoregressive conditional heteroskedasticity Order (group theory) Recurrence equations Recursion (computer science) Applied mathematics Statistics Probability and Uncertainty Stationary solution Mathematics
Zdroj:	Journal of Theoretical Probability. 34:1831-1869
ISSN:	1572-9230 0894-9840
DOI:	10.1007/s10959-020-01019-8
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::dda9c16cfd865fbcfae3c0383bb35351 https://doi.org/10.1007/s10959-020-01019-8 Zobrazit plný text záznamu Full text from SpringerLink