IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v35y2020i4d10.1007_s00180-020-00982-4.html
   My bibliography  Save this article

A time series model based on dependent zero inflated counting series

Author

Listed:
  • Nisreen Shamma

    (University of Mazandaran)

  • Mehrnaz Mohammadpour

    (University of Mazandaran)

  • Masoumeh Shirozhan

    (University of Mazandaran)

Abstract

In this paper, we introduce a new generalized negative binomial thinning operator with dependent counting series. Some properties of the thinning operator are derived. A new stationary integer-valued autoregressive model based on the thinning operator is constructed. In addition various properties of the process are determined, unknown parameters are estimated by several methods and the behavior of the estimators is described through the numerical results. Also, the model is applied on a real data set and compared to some relevant INAR(1) models.

Suggested Citation

  • Nisreen Shamma & Mehrnaz Mohammadpour & Masoumeh Shirozhan, 2020. "A time series model based on dependent zero inflated counting series," Computational Statistics, Springer, vol. 35(4), pages 1737-1757, December.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00982-4
    DOI: 10.1007/s00180-020-00982-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-020-00982-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-020-00982-4?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. A. Alzaid & M. Al‐Osh, 1988. "First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 42(1), pages 53-61, March.
    2. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    3. Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
    4. A. Alzaid & M. Al-Osh, 1993. "Some autoregressive moving average processes with generalized Poisson marginal distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 223-232, June.
    5. Borges, Patrick & Molinares, Fabio Fajardo & Bourguignon, Marcelo, 2016. "A geometric time series model with inflated-parameter Bernoulli counting series," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 264-272.
    6. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, July.
    7. Claudia Czado & Tilmann Gneiting & Leonhard Held, 2009. "Predictive Model Assessment for Count Data," Biometrics, The International Biometric Society, vol. 65(4), pages 1254-1261, December.
    8. Robert C. Jung & A. R. Tremayne, 2011. "Convolution‐closed models for count time series with applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 268-280, May.
    9. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
    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. Shirozhan, M. & Bakouch, Hassan S. & Mohammadpour, M., 2023. "A flexible INAR(1) time series model with dependent zero-inflated count series and medical contagious cases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 216-230.

    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. Shirozhan, M. & Bakouch, Hassan S. & Mohammadpour, M., 2023. "A flexible INAR(1) time series model with dependent zero-inflated count series and medical contagious cases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 216-230.
    2. Wooi Chen Khoo & Seng Huat Ong & Atanu Biswas, 2017. "Modeling time series of counts with a new class of INAR(1) model," Statistical Papers, Springer, vol. 58(2), pages 393-416, June.
    3. Miroslav M. Ristić & Aleksandar S. Nastić & Ana V. Miletić Ilić, 2013. "A geometric time series model with dependent Bernoulli counting series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 466-476, July.
    4. José M. R. Murteira & Mário A. G. Augusto, 2017. "Hurdle models of repayment behaviour in personal loan contracts," Empirical Economics, Springer, vol. 53(2), pages 641-667, September.
    5. Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
    6. Yousung Park & Hee-Young Kim, 2012. "Diagnostic checks for integer-valued autoregressive models using expected residuals," Statistical Papers, Springer, vol. 53(4), pages 951-970, November.
    7. Manik Awale & N. Balakrishna & T. V. Ramanathan, 2019. "Testing the constancy of the thinning parameter in a random coefficient integer autoregressive model," Statistical Papers, Springer, vol. 60(5), pages 1515-1539, October.
    8. Kimberly F. Sellers & Ali Arab & Sean Melville & Fanyu Cui, 2021. "A flexible univariate moving average time-series model for dispersed count data," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-12, December.
    9. Layth C. Alwan & Christian H. Weiß, 2017. "INAR implementation of newsvendor model for serially dependent demand counts," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1085-1099, February.
    10. Nastić, Aleksandar S. & Ristić, Miroslav M., 2012. "Some geometric mixed integer-valued autoregressive (INAR) models," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 805-811.
    11. Shihang Yu & Dehui Wang & Xia Chen, 2018. "Large and Moderate Deviations for the Total Population Arising from a Sub-critical Galton–Watson Process with Immigration," Journal of Theoretical Probability, Springer, vol. 31(1), pages 41-67, March.
    12. Robert C. Jung & Andrew R. Tremayne, 2020. "Maximum-Likelihood Estimation in a Special Integer Autoregressive Model," Econometrics, MDPI, vol. 8(2), pages 1-15, June.
    13. Marcelo Bourguignon, 2016. "Poisson–geometric INAR(1) process for modeling count time series with overdispersion," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(3), pages 176-192, August.
    14. Boris Aleksandrov & Christian H. Weiß, 2020. "Testing the dispersion structure of count time series using Pearson residuals," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 325-361, September.
    15. Marcelo Bourguignon & Christian H. Weiß, 2017. "An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 847-868, December.
    16. Raju Maiti & Atanu Biswas & Bibhas Chakraborty, 2018. "Modelling of low count heavy tailed time series data consisting large number of zeros and ones," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 407-435, August.
    17. Johannes Ferreira & Ané van der Merwe, 2022. "A Noncentral Lindley Construction Illustrated in an INAR(1) Environment," Stats, MDPI, vol. 5(1), pages 1-19, January.
    18. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2017. "Tests for Structural Changes in Time Series of Counts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 843-865, December.
    19. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
    20. Hassan Bakouch & Miroslav Ristić, 2010. "Zero truncated Poisson integer-valued AR(1) model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 265-280, September.

    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:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00982-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.