This paper provides a least squares regression estimation of the tail index for long memory processes where the innovations are \(\alpha \)-stable random sequences. The estimate is based on the property of the characteristic function of the process near the origin. The asymptotics of the estimator are obtained by choosing suitable regression samples with the help of the properties of the \(\alpha \)-stable distribution. The numerical simulation and an empirical analysis of financial market data are conducted to assess the finite sample performance of the proposed estimator.

中文翻译：

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长记忆进程的尾部索引估计

本文提供了长记忆过程尾部指数的最小二乘回归估计，其创新之处在于\(\alpha \)-稳定的随机序列。该估计基于原点附近过程的特征函数的性质。借助 \(\alpha \) 稳定分布的性质，通过选择合适的回归样本来获得估计量的渐进性。通过数值模拟和金融市场数据的实证分析来评估所提出的估计器的有限样本性能。