IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i5d10.1007_s00362-017-0884-x.html
   My bibliography  Save this article

Testing the constancy of the thinning parameter in a random coefficient integer autoregressive model

Author

Listed:
  • Manik Awale

    (Savitribai Phule Pune University)

  • N. Balakrishna

    (Cochin University of Science and Technology)

  • T. V. Ramanathan

    (Savitribai Phule Pune University)

Abstract

Integer-valued autoregressive models are widely used for modeling the time dependent count data. Many of the inference problems related to these types of models are not yet addressed due to the complexities of the related distribution theory. In this paper, we consider one such inference problem associated with these types of models. For a random coefficient integer-valued autoregressive model, we develop a locally most powerful-type test for testing the hypothesis that the thinning parameter is constant across the time. The asymptotic distribution of the suggested test statistic is derived. The Poisson and geometric INAR(1) models are considered for the illustration of the suggested methodology. Simulation studies indicate that the suggested test performs quite well. We have applied our methods to count time series data sets, where the thinning parameter is suspected to be varying.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0884-x
    DOI: 10.1007/s00362-017-0884-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0884-x
    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/s00362-017-0884-x?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. Nadjib Bouzar & K. Jayakumar, 2008. "Time series with discrete semistable marginals," Statistical Papers, Springer, vol. 49(4), pages 619-635, October.
    2. Akanksha S. Kashikar & Neelabh Rohan & T.V. Ramanathan, 2013. "Integer autoregressive models with structural breaks," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2653-2669, December.
    3. 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.
    4. 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.
    5. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    6. 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.
    7. Raju Maiti & Atanu Biswas & Samarjit Das, 2015. "Time Series of Zero‐Inflated Counts and their Coherent Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(8), pages 694-707, December.
    8. Simos Meintanis & Dimitris Karlis, 2014. "Validation tests for the innovation distribution in INAR time series models," Computational Statistics, Springer, vol. 29(5), pages 1221-1241, October.
    9. Christian Weiß & Hee-Young Kim, 2013. "Parameter estimation for binomial AR(1) models with applications in finance and industry," Statistical Papers, Springer, vol. 54(3), pages 563-590, August.
    10. Lu Han & Brendan McCabe, 2013. "Testing for parameter constancy in non-Gaussian time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 17-29, January.
    11. Jiwon Kang & Sangyeol Lee, 2009. "Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 239-258, March.
    12. Haitao Zheng & Ishwar V. Basawa & Somnath Datta, 2006. "Inference for pth‐order random coefficient integer‐valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 411-440, May.
    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. Kai Yang & Han Li & Dehui Wang & Chenhui Zhang, 2021. "Random coefficients integer-valued threshold autoregressive processes driven by logistic regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 533-557, December.
    2. Li Bi & Deqi Wang & Libo Cheng & Dequan Qi, 2024. "Testing Coefficient Randomness in Multivariate Random Coefficient Autoregressive Models Based on Locally Most Powerful Test," Mathematics, MDPI, vol. 12(16), pages 1-21, August.
    3. Feilong Lu & Dehui Wang, 2022. "A new estimation for INAR(1) process with Poisson distribution," Computational Statistics, Springer, vol. 37(3), pages 1185-1201, July.

    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. 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.
    2. Wagner Barreto-Souza, 2015. "Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 839-852, November.
    3. Feilong Lu & Dehui Wang, 2022. "A new estimation for INAR(1) process with Poisson distribution," Computational Statistics, Springer, vol. 37(3), pages 1185-1201, July.
    4. Jentsch, Carsten & Weiß, Christian, 2017. "Bootstrapping INAR models," Working Papers 17-02, University of Mannheim, Department of Economics.
    5. Shengqi Tian & Dehui Wang & Shuai Cui, 2020. "A seasonal geometric INAR process based on negative binomial thinning operator," Statistical Papers, Springer, vol. 61(6), pages 2561-2581, December.
    6. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2021. "Goodness–of–Fit Tests for Bivariate Time Series of Counts," Econometrics, MDPI, vol. 9(1), pages 1-20, March.
    7. Christian H. Weiß & Annika Homburg & Pedro Puig, 2019. "Testing for zero inflation and overdispersion in INAR(1) models," Statistical Papers, Springer, vol. 60(3), pages 823-848, June.
    8. Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.
    9. 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.
    10. repec:tiu:tiutis:6b90fe6f-4de9-4192-9f4d-99ae9220af75 is not listed on IDEAS
    11. Subhankar Chattopadhyay & Raju Maiti & Samarjit Das & Atanu Biswas, 2022. "Change‐point analysis through integer‐valued autoregressive process with application to some COVID‐19 data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 4-34, February.
    12. Aleksandar S. Nastić & Petra N. Laketa & Miroslav M. Ristić, 2016. "Random environment integer-valued autoregressive process," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 267-287, March.
    13. 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.
    14. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    15. 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.
    16. 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.
    17. Sebastian Schweer & Christian H. Weiß, 2016. "Testing for Poisson arrivals in INAR(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 503-524, September.
    18. Sebastian Schweer, 2016. "A Goodness-of-Fit Test for Integer-Valued Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 77-98, January.
    19. 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.
    20. 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.
    21. Boris Aleksandrov & Christian H. Weiß & Simon Nik & Maxime Faymonville & Carsten Jentsch, 2024. "Modelling and diagnostic tests for Poisson and negative-binomial count time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 843-887, October.

    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:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0884-x. 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.