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A new BISARMA time series model for forecasting mortality using weather and particulate matter data

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  • Víctor Leiva
  • Helton Saulo
  • Rubens Souza
  • Robert G. Aykroyd
  • Roberto Vila

Abstract

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.

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  • Víctor Leiva & Helton Saulo & Rubens Souza & Robert G. Aykroyd & Roberto Vila, 2021. "A new BISARMA time series model for forecasting mortality using weather and particulate matter data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 346-364, March.
    • Handle: RePEc:wly:jforec:v:40:y:2021:i:2:p:346-364
    DOI: 10.1002/for.2718
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    References listed on IDEAS

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    1. Victor Leiva & Carolina Marchant & Fabrizio Ruggeri & Helton Saulo, 2015. "A criterion for environmental assessment using Birnbaum–Saunders attribute control charts," Environmetrics, John Wiley & Sons, Ltd., vol. 26(7), pages 463-476, November.
    2. Benjamin M.A. & Rigby R.A. & Stasinopoulos D.M., 2003. "Generalized Autoregressive Moving Average Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 214-223, January.
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    5. Rodney V. Fonseca & Francisco Cribari-Neto, 2018. "Bimodal Birnbaum–Saunders generalized autoregressive score model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(14), pages 2585-2606, October.
    6. N. Balakrishnan & Debasis Kundu, 2019. "Birnbaum‐Saunders distribution: A review of models, analysis, and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(1), pages 4-49, January.
    7. Camilo Lillo & Víctor Leiva & Orietta Nicolis & Robert G. Aykroyd, 2018. "L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 187-209, January.
    8. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    9. Souhir Ben Amor & Heni Boubaker & Lotfi Belkacem, 2018. "Forecasting electricity spot price for Nord Pool market with a hybrid k‐factor GARMA–LLWNN model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(8), pages 832-851, December.
    10. Xiang Xu, 2020. "Forecasting air pollution PM2.5 in Beijing using weather data and multiple kernel learning," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 117-125, March.
    11. Marcelo Ventura & Helton Saulo & Victor Leiva & Sandro Monsueto, 2019. "Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(4), pages 963-977, July.
    12. T. Rahul & N. Balakrishnan & N. Balakrishna, 2018. "Time series with Birnbaum‐Saunders marginal distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(4), pages 562-581, July.
    13. Carolina Marchant & Víctor Leiva & Francisco José A. Cysneiros & Juan F. Vivanco, 2016. "Diagnostics in multivariate generalized Birnbaum-Saunders regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2829-2849, November.
    14. Robert G. Aykroyd & Víctor Leiva & Carolina Marchant, 2018. "Multivariate Birnbaum-Saunders Distributions: Modelling and Applications," Risks, MDPI, vol. 6(1), pages 1-25, March.
    15. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    16. Carolina Marchant & Víctor Leiva & George Christakos & M. Fernanda Cavieres, 2019. "Monitoring urban environmental pollution by bivariate control charts: New methodology and case study in Santiago, Chile," Environmetrics, John Wiley & Sons, Ltd., vol. 30(5), August.
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    3. Jorge I. Figueroa-Zúñiga & Cristian L. Bayes & Víctor Leiva & Shuangzhe Liu, 2022. "Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications," Statistical Papers, Springer, vol. 63(3), pages 919-942, June.
    4. Luis Sánchez & Víctor Leiva & Helton Saulo & Carolina Marchant & José M. Sarabia, 2021. "A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications," Mathematics, MDPI, vol. 9(21), pages 1-21, November.
    5. Jimmy Reyes & Jaime Arrué & Víctor Leiva & Carlos Martin-Barreiro, 2021. "A New Birnbaum–Saunders Distribution and Its Mathematical Features Applied to Bimodal Real-World Data from Environment and Medicine," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    6. Hanns de la Fuente-Mella & Rolando Rubilar & Karime Chahuán-Jiménez & Víctor Leiva, 2021. "Modeling COVID-19 Cases Statistically and Evaluating Their Effect on the Economy of Countries," Mathematics, MDPI, vol. 9(13), pages 1-13, July.

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