IDEAS home Printed from https://ideas.repec.org/a/wly/jforec/v40y2021i2p346-364.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/for.2718
    Download Restriction: no
    File URL: https://libkey.io/10.1002/for.2718?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. A. I. McLeod & Y. Zhang, 2006. "Partial autocorrelation parameterization for subset autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 599-612, July.
    3. Andréa Rocha & Francisco Cribari-Neto, 2009. "Beta autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 529-545, November.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    12. 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.
    13. 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.
    14. 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.
    15. Robert G. Aykroyd & Víctor Leiva & Carolina Marchant, 2018. "Multivariate Birnbaum-Saunders Distributions: Modelling and Applications," Risks, MDPI, vol. 6(1), pages 1-25, March.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Raydonal Ospina & João A. M. Gondim & Víctor Leiva & Cecilia Castro, 2023. "An Overview of Forecast Analysis with ARIMA Models during the COVID-19 Pandemic: Methodology and Case Study in Brazil," Mathematics, MDPI, vol. 11(14), pages 1-18, July.
    2. 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.
    3. 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.
    4. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    5. 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.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    2. 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.
    3. Saulo, Helton & Balakrishnan, Narayanaswamy & Vila, Roberto, 2023. "On a quantile autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 425-448.
    4. Tingguo Zheng & Han Xiao & Rong Chen, 2022. "Generalized autoregressive moving average models with GARCH errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 125-146, January.
    5. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2021. "Autoregressive conditional proportion: A multiplicative-error model for (0,1)-valued time series," MPRA Paper 110954, University Library of Munich, Germany, revised 06 Dec 2021.
    6. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    7. Helton Saulo & Jeremias Leão & Víctor Leiva & Robert G. Aykroyd, 2019. "Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data," Statistical Papers, Springer, vol. 60(5), pages 1605-1629, October.
    8. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2020. "Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    9. Tingguo Zheng & Han Xiao & Rong Chen, 2021. "Generalized Autoregressive Moving Average Models with GARCH Errors," Papers 2105.05532, arXiv.org.
    10. Abdelhakim Aknouche & Stefanos Dimitrakopoulos, 2023. "Autoregressive conditional proportion: A multiplicative‐error model for (0,1)‐valued time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 393-417, July.
    11. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2006. "Vector Multiplicative Error Models: Representation and Inference," NBER Technical Working Papers 0331, National Bureau of Economic Research, Inc.
    12. Robert G. Aykroyd & Víctor Leiva & Carolina Marchant, 2018. "Multivariate Birnbaum-Saunders Distributions: Modelling and Applications," Risks, MDPI, vol. 6(1), pages 1-25, March.
    13. Gómez-Déniz, E. & Pérez-Rodríguez, J.V., 2019. "Modelling bimodality of length of tourist stay," Annals of Tourism Research, Elsevier, vol. 75(C), pages 131-151.
    14. Shamsuzzaman, Mohammad & Shamsuzzoha, Ahm & Maged, Ahmed & Haridy, Salah & Bashir, Hamdi & Karim, Azharul, 2021. "Effective monitoring of carbon emissions from industrial sector using statistical process control," Applied Energy, Elsevier, vol. 300(C).
    15. Alejandra Tapia & Viviana Giampaoli & Víctor Leiva & Yuhlong Lio, 2020. "Data-Influence Analytics in Predictive Models Applied to Asthma Disease," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    16. Zheng, Tingguo & Chen, Rong, 2017. "Dirichlet ARMA models for compositional time series," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 31-46.
    17. Pooi AH-HIN & Ng KOK-HAUR & Soo HUEI-CHING, 2016. "Modelling and Forecasting with Financial Duration Data Using Non-linear Model," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(2), pages 79-92.
    18. Guilherme Pumi & Taiane Schaedler Prass & Rafael Rigão Souza, 2021. "A dynamic model for double‐bounded time series with chaotic‐driven conditional averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 68-86, March.
    19. Abraão D. C. Nascimento & Maria C. S. Lima & Hassan Bakouch & Najla Qarmalah, 2023. "Scaled Muth–ARMA Process Applied to Finance Market," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    20. Aykroyd, Robert G. & Leiva, Víctor & Ruggeri, Fabrizio, 2019. "Recent developments of control charts, identification of big data sources and future trends of current research," Technological Forecasting and Social Change, Elsevier, vol. 144(C), pages 221-232.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jforec:v:40:y:2021:i:2:p:346-364. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/2966 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.