CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH

研究问题: 高斯创新的多元 BEKK–ARCH 过程何时存在严格平稳且遍历的解，其不同分量能否具有不同的重尾指数？
方法与思路: 作者利用多元随机递推方程表示研究平稳性和尾部，允许多个滞后进入条件协方差，并用加密货币日收益说明。
材料陈述的贡献: 摘要称在所述条件下存在可能仅有分数阶矩的平稳解，各分量具有正则变化尾部，且尾指数一般可以不同。
阅读关注点: 应核对平稳与遍历条件、分量正则变化的证明、尾指数的求解方式，以及两种加密货币应用中模型拟合的限制。
阅读边界: 仅据所给 Crossref 摘要，结论针对指定的高斯创新 BEKK–ARCH 类，不能泛化到任意 BEKK 或 GARCH；版本变化未说明。

GPT-6.1 Sol · 高 · 2026-10-03

原文摘要

We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes $(X_t : t=1,2,\ldots )$ and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged $X_t$ ’s may load into the conditional covariance matrix of $X_t$ . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of $X_t$ may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes $(X_t : t=1,2,\ldots )$ and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged $X_t$ ’s may load into the conditional covariance matrix of $X_t$ . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of $X_t$ may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.

摘要来源：Crossref

笔记与分组

分类依据与纠错

CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH

代码、数据与补充材料

一类 BEKK 过程的尾部行为：随机递推方程方法

原文摘要

同方向的基础文献

同方向的基础文献