IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v29y2014i5p1221-1241.html
   My bibliography  Save this article

Validation tests for the innovation distribution in INAR time series models

Author

Listed:
  • Simos Meintanis
  • Dimitris Karlis

Abstract

Goodness-of-fit tests are proposed for the innovation distribution in INAR models. The test statistics incorporate the joint probability generating function of the observations. Special emphasis is given to the INAR(1) model and particular instances of the procedures which involve innovations from the general family of Poisson stopped-sum distributions. A Monte Carlo power study of a bootstrap version of the test statistic is included as well as a real data example. Generalizations of the proposed methods are also discussed. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:1221-1241
    DOI: 10.1007/s00180-014-0488-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-014-0488-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-014-0488-z?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. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Anne Leucht & Michael Neumann, 2013. "Degenerate $$U$$ - and $$V$$ -statistics under ergodicity: asymptotics, bootstrap and applications in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 349-386, April.
    3. V. Savani & A. Zhigljavsky, 2007. "Efficient parameter estimation for independent and INAR(1) negative binomial samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 207-225, February.
    4. 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.
    5. Simos Meintanis, 2008. "New inference procedures for generalized Poisson distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 751-762.
    6. Meintanis, Simos & Swanepoel, Jan, 2007. "Bootstrap goodness-of-fit tests with estimated parameters based on empirical transforms," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1004-1013, June.
    7. Leucht, Anne, 2012. "Characteristic function-based hypothesis tests under weak dependence," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 67-89.
    8. Jean–Claude Massé & Radu Theodorescu, 2005. "Neyman type A distribution revisited," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(2), pages 206-213, 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. Masoomeh Forughi & Zohreh Shishebor & Atefeh Zamani, 2022. "Portmanteau tests for generalized integer-valued autoregressive time series models," Statistical Papers, Springer, vol. 63(4), pages 1163-1185, August.
    2. Christian H. Weiß, 2018. "Goodness-of-fit testing of a count time series’ marginal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 619-651, August.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. Jentsch, Carsten & Weiß, Christian, 2017. "Bootstrapping INAR models," Working Papers 17-02, University of Mannheim, Department of Economics.
    9. 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.
    10. 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.
    11. Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.
    12. Lucio Palazzo & Riccardo Ievoli, 2022. "A Semiparametric Approach to Test for the Presence of INAR: Simulations and Empirical Applications," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    13. 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.

    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. Cathy W. S. Chen & Sangyeol Lee, 2017. "Bayesian causality test for integer-valued time series models with applications to climate and crime data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 797-814, August.
    2. Youngmi Lee & Sangyeol Lee, 2019. "CUSUM test for general nonlinear integer-valued GARCH models: comparison study," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1033-1057, October.
    3. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
    4. Jentsch, Carsten & Leucht, Anne, 2014. "Bootstrapping Sample Quantiles of Discrete Data," Working Papers 14-15, University of Mannheim, Department of Economics.
    5. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    6. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    7. Yan Cui & Qi Li & Fukang Zhu, 2020. "Flexible bivariate Poisson integer-valued GARCH model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1449-1477, December.
    8. Huaping Chen & Qi Li & Fukang Zhu, 2022. "A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 243-270, June.
    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. Youngmi Lee & Sangyeol Lee & Dag Tjøstheim, 2018. "Asymptotic normality and parameter change test for bivariate Poisson INGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 52-69, March.
    11. Weiß, Christian H., 2010. "INARCH(1) processes: Higher-order moments and jumps," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1771-1780, December.
    12. 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.
    13. Weiß, Christian H. & Zhu, Fukang, 2024. "Conditional-mean multiplicative operator models for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    14. 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.
    15. Leucht, Anne & Neumann, Michael H., 2013. "Dependent wild bootstrap for degenerate U- and V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 257-280.
    16. Kang, Jiwon & Lee, Sangyeol, 2014. "Minimum density power divergence estimator for Poisson autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 44-56.
    17. E. Gonçalves & N. Mendes-Lopes & F. Silva, 2015. "Infinitely Divisible Distributions in Integer-Valued Garch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 503-527, July.
    18. Dante Amengual & Marine Carrasco & Enrique Sentana, 2017. "Testing Distributional Assumptions Using a Continuum of Moments," Working Papers wp2018_1709, CEMFI.
    19. Jon Michel, 2020. "The Limiting Distribution of a Non‐Stationary Integer Valued GARCH(1,1) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 351-356, March.
    20. Zeng, Xiaoqiang & Kakizawa, Yoshihide, 2024. "Two-step conditional least squares estimation in ADCINAR(1) process, revisited," Statistics & Probability Letters, Elsevier, vol. 206(C).

    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:29:y:2014:i:5:p:1221-1241. 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.