The Birnbaum–Saunders (BS) distribution is a model that frequently appears in the statistical literature and has proved to be very versatile and efficient across a wide range of applications. However, despite the growing interest in the study of this distribution and the development of many articles, few of them have considered data with a dependency structure. To fill this gap, we introduce a new class of time series models based on the BS distribution, which allows modeling of positive and asymmetric data that have an autoregressive structure. We call these BS autoregressive moving average (BISARMA) models. Also included is a thorough study of theoretical properties of the proposed methodology and of practical issues, such as maximum likelihood parameter estimation, diagnostic analytics, and prediction. The performance of the proposed methodology is evaluated using Monte Carlo simulations. An analysis of real‐world data is performed using the methodology to show its potential for applications. The numerical results report the excellent performance of the BISARMA model, indicating that the BS distribution is a good modeling choice when dealing with time series data with positive support and asymmetrically distributed. Hence, it can be a valuable addition to the toolkit of applied statisticians and data scientists.

中文翻译：

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一种新的BISARMA时间序列模型，可使用天气和颗粒物数据预测死亡率

Birnbaum–Saunders（BS）分布是一种统计模型中经常出现的模型，并且已被证明在多种应用中非常通用且高效。但是，尽管人们对这种分布的研究和许多文章的发展越来越感兴趣，但很少有人考虑具有依赖结构的数据。为了填补这一空白，我们引入了基于BS分布的一类新的时间序列模型，该模型允许对具有自回归结构的正向和非对称数据进行建模。我们称这些BS自回归移动平均（BISARMA）模型。还包括对所提出方法的理论性质和实际问题（例如最大似然参数估计，诊断分析和预测）进行彻底研究。使用蒙特卡洛模拟评估了所提出方法的性能。使用该方法对真实数据进行分析，以显示其应用潜力。数值结果表明，BISARMA模型具有出色的性能，表明当处理具有正支撑和不对称分布的时间序列数据时，BS分布是一个很好的建模选择。因此，它可能是对应用统计学家和数据科学家的工具包的宝贵补充。表明在处理具有正支持和非对称分布的时间序列数据时，BS分布是一个很好的建模选择。因此，它可能是对应用统计学家和数据科学家的工具包的宝贵补充。表明在处理具有正支持和非对称分布的时间序列数据时，BS分布是一个很好的建模选择。因此，它可能是对应用统计学家和数据科学家的工具包的宝贵补充。