Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach

2019/02/22 by Muneya Matsui, Matsui, Muneya, Rasmus Søndergaard Pedersen +1 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1902.08364

openalex publication_date 2019/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We provide new, mild conditions for strict stationarity and ergodicity of a class of BEKK processes. By exploiting that the processes can be represented as multivariate stochastic recurrence equations, we characterize the tail behavior of the associated stationary laws. Specifically, we show that the each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts most of the existing literature on the tail behavior of multivariate GARCH processes.

Citations

• Tail indices for AX+B recursion with triangular matrices

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