IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v164y2023icp1-32.html
   My bibliography  Save this article

Fluctuations and precise deviations of cumulative INAR time series

Author

Listed:
  • Kirchner, Matthias
  • Torrisi, Giovanni Luca

Abstract

In this paper, we study fluctuations and precise deviations of cumulative INAR time series, both in a non-stationary and in a stationary regime. The theoretical results are based on the recent mod-ϕ convergence theory as presented in Féray et al., 2016. We apply our findings to the construction of approximate confidence intervals for model parameters and to quantile calculation in a risk management context.

Suggested Citation

  • Kirchner, Matthias & Torrisi, Giovanni Luca, 2023. "Fluctuations and precise deviations of cumulative INAR time series," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 1-32.
    • Handle: RePEc:eee:spapps:v:164:y:2023:i:c:p:1-32
    DOI: 10.1016/j.spa.2023.07.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414923001370
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2023.07.002?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. Torrisi, Giovanni Luca & Leonardi, Emilio, 2022. "Asymptotic analysis of Poisson shot noise processes, and applications," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 229-270.
    3. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    4. Jonas Andersson & Dimitris Karlis, 2010. "Treating missing values in INAR(1) models: An application to syndromic surveillance data," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 12-19, January.
    5. Yunwei Cui & Robert Lund, 2009. "A new look at time series of counts," Biometrika, Biometrika Trust, vol. 96(4), pages 781-792.
    6. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    7. Weiß, Christian H., 2008. "The combined INAR(p) models for time series of counts," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1817-1822, September.
    8. Blundell, Richard & Griffith, Rachel & Windmeijer, Frank, 2002. "Individual effects and dynamics in count data models," Journal of Econometrics, Elsevier, vol. 108(1), pages 113-131, May.
    9. Lambert, Diane & Liu, Chuanhai, 2006. "Adaptive Thresholds: Monitoring Streams of Network Counts," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 78-88, March.
    10. Benjamin Kedem & Konstantinos Fokianos, 2002. "Regression Models for Binary Time Series," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 185-199, Springer.
    11. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    12. Rong Zhu & Harry Joe, 2006. "Modelling Count Data Time Series with Markov Processes Based on Binomial Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 725-738, September.
    Full references (including those not matched with items on IDEAS)

    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. Wagner Barreto‐Souza & Hernando Ombao, 2022. "The negative binomial process: A tractable model with composite likelihood‐based inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 568-592, June.
    2. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    3. Aknouche, Abdelhakim & Francq, Christian, 2021. "Count And Duration Time Series With Equal Conditional Stochastic And Mean Orders," Econometric Theory, Cambridge University Press, vol. 37(2), pages 248-280, April.
    4. Byungsoo Kim & Sangyeol Lee, 2020. "Robust estimation for general integer-valued time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1371-1396, December.
    5. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    6. Aknouche, Abdelhakim & Scotto, Manuel, 2022. "A multiplicative thinning-based integer-valued GARCH model," MPRA Paper 112475, University Library of Munich, Germany.
    7. 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.
    8. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    10. Lee, Sangyeol & Kim, Dongwon & Kim, Byungsoo, 2023. "Modeling and inference for multivariate time series of counts based on the INGARCH scheme," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    11. Paul Doukhan & Konstantinos Fokianos & Joseph Rynkiewicz, 2021. "Mixtures of Nonlinear Poisson Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(1), pages 107-135, January.
    12. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    13. 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.
    14. Huiyu Mao & Fukang Zhu & Yan Cui, 2020. "A generalized mixture integer-valued GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 527-552, September.
    15. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    16. Hanan Elsaied & Roland Fried, 2014. "Robust Fitting Of Inarch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 517-535, November.
    17. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    18. William Kengne & Isidore S. Ngongo, 2022. "Inference for nonstationary time series of counts with application to change-point problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 801-835, August.
    19. Christian H. Weiß & Esmeralda Gonçalves & Nazaré Mendes Lopes, 2017. "Testing the compounding structure of the CP-INARCH model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 571-603, July.
    20. Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.

    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:eee:spapps:v:164:y:2023:i:c:p:1-32. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.