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.
- ARMA models
- Birnbaum–Saunders distribution
- data dependent over time
- maximum likelihood and Monte Carlo methods
- model selection
- R software