This article proposes a new approach to the conditional autoregressive range (CARR) model using the Birnbaum‐Saunders (BS) distribution. The model aims to develop volatility clustering, which incorporates extreme fluctuations, using a time‐varying evolution of the range process called the BSCARR model. Furthermore, diagnosis analysis tools for diagnosis analysis were developed to evaluate the goodness of fit, such as residual analysis, global influence measures based on Cook's distance, and local influence analysis. For illustrative purposes, three real financial market indices are analyzed. A comparison with classical CARR models was also carried out in these examples. The results indicated that the proposed model outperformed some existing models in the literature, especially a recent CARR model based on the gamma distribution even under the presence of atypical cases (observed values).

中文翻译：

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Birnbaum-Saunders自回归条件范围模型应用于股票指数数据

本文提出了一种使用Birnbaum-Saunders（BS）分布的条件自回归范围（CARR）模型的新方法。该模型旨在利用称为BSCARR模型的范围变化过程随时间变化，发展包含极端波动的波动性聚类。此外，开发了用于诊断分析的诊断分析工具以评估拟合的优劣，例如残差分析，基于库克距离的全局影响量度和局部影响分析。为了说明的目的，分析了三个真实的金融市场指数。在这些示例中，还与经典CARR模型进行了比较。结果表明，所提出的模型优于文献中已有的模型，