IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v29y2008i5p783-801.html
   My bibliography  Save this article

Local asymptotic normality and efficient estimation for INAR(p) models

Author

Listed:
  • Feike C. Drost
  • Ramon Van Den Akker
  • Bas J. M. Werker

Abstract

. Integer‐valued autoregressive (INAR) processes have been introduced to model non‐negative integer‐valued phenomena that evolve in time. The distribution of an INAR(p) process is determined by two parameters: a vector of survival probabilities and a probability distribution on the non‐negative integers, called an immigration distribution. This paper provides an efficient estimator of the parameters, and in particular, shows that the INAR(p) model has the Local Asymptotic Normality property.

Suggested Citation

  • Feike C. Drost & Ramon Van Den Akker & Bas J. M. Werker, 2008. "Local asymptotic normality and efficient estimation for INAR(p) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 783-801, September.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:5:p:783-801
    DOI: 10.1111/j.1467-9892.2008.00581.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2008.00581.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2008.00581.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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kurt Brannas & Jorgen Hellstrom, 2001. "Generalized Integer-Valued Autoregression," Econometric Reviews, Taylor & Francis Journals, vol. 20(4), pages 425-443.
    2. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    3. Alain Latour, 1998. "Existence and Stochastic Structure of a Non‐negative Integer‐valued Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 439-455, July.
    4. Maria Eduarda Silva & Vera Lúcia Oliveira, 2005. "Difference Equations for the Higher Order Moments and Cumulants of the INAR(p) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 17-36, January.
    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. Drost, Feike C. & van den Akker, Ramon & Werker, Bas J.M., 2008. "Note on integer-valued bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 992-996, June.
    7. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "An Asymptotic Analysis of Nearly Unstable inar (1) Models," Other publications TiSEM 6e89d2b0-1d07-4f01-9b2f-5, Tilburg University, School of Economics and Management.
    8. Elisabet Berglund & Kurt Brännäs, 2001. "Plants' entry and exit in Swedish municipalities," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 35(3), pages 431-448.
    9. Nikas Rudholm, 2001. "Entry and the Number of Firms in the Swedish Pharmaceuticals Market," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 19(3), pages 351-364, November.
    10. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "An Asymptotic Analysis of Nearly Unstable inar (1) Models," Discussion Paper 2006-44, Tilburg University, Center for Economic Research.
    11. 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.
    12. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2008. "Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)," Discussion Paper 2008-53, Tilburg University, Center for Economic Research.
    13. Gourieroux, C. & Jasiak, J., 2004. "Heterogeneous INAR(1) model with application to car insurance," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 177-192, April.
    14. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
    15. Ulf Böckenholt, 2003. "Analysing state dependences in emotional experiences by dynamic count data models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(2), pages 213-226, 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. Mohamed Sadoun & Mohamed Bentarzi, 2021. "Locally asymptotically efficient estimation for parametric PINAR(p) models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 257-289, August.
    2. Feike C. Drost & Ramon van den Akker & Bas J. M. Werker, 2009. "Efficient estimation of auto‐regression parameters and innovation distributions for semiparametric integer‐valued AR(p) models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 467-485, April.
    3. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "An Asymptotic Analysis of Nearly Unstable inar (1) Models," Other publications TiSEM 6e89d2b0-1d07-4f01-9b2f-5, Tilburg University, School of Economics and Management.
    4. repec:tiu:tiutis:6b90fe6f-4de9-4192-9f4d-99ae9220af75 is not listed on IDEAS
    5. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2009. "The asymptotic structure of nearly unstable non negative integer-valued AR(1) models," Other publications TiSEM ac0494ae-7a32-43ca-b5b4-d, Tilburg University, School of Economics and Management.
    6. Mátyás Barczy & Márton Ispány & Gyula Pap, 2014. "Asymptotic Behavior of Conditional Least Squares Estimators for Unstable Integer-valued Autoregressive Models of Order 2," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 866-892, December.
    7. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "An Asymptotic Analysis of Nearly Unstable inar (1) Models," Discussion Paper 2006-44, Tilburg University, Center for Economic Research.
    8. Ruijun Bu & Brendan McCabe & Kaddour Hadri, 2008. "Maximum likelihood estimation of higher‐order integer‐valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 973-994, 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. Francesco Bravo, 2011. "Comment on: Subsampling weakly dependent time series and application to extremes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 483-486, November.
    2. repec:tiu:tiutis:6b90fe6f-4de9-4192-9f4d-99ae9220af75 is not listed on IDEAS
    3. Feike C. Drost & Ramon van den Akker & Bas J. M. Werker, 2009. "Efficient estimation of auto‐regression parameters and innovation distributions for semiparametric integer‐valued AR(p) models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 467-485, April.
    4. Isabel Silva & M. Eduarda Silva & Isabel Pereira & Nélia Silva, 2005. "Replicated INAR(1) Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 517-542, December.
    5. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2009. "The asymptotic structure of nearly unstable non negative integer-valued AR(1) models," Other publications TiSEM ac0494ae-7a32-43ca-b5b4-d, Tilburg University, School of Economics and Management.
    6. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2008. "Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)," Other publications TiSEM cef533d0-6b49-4ce9-8cd2-7, Tilburg University, School of Economics and Management.
    7. 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.
    8. Mirko Armillotta & Paolo Gorgi, 2023. "Pseudo-variance quasi-maximum likelihood estimation of semi-parametric time series models," Tinbergen Institute Discussion Papers 23-054/III, Tinbergen Institute.
    9. Giulia Carallo & Roberto Casarin & Christian P. Robert, 2020. "Generalized Poisson Difference Autoregressive Processes," Papers 2002.04470, arXiv.org.
    10. Kristensen, Dennis & Rahbek, Anders, 2010. "Likelihood-based inference for cointegration with nonlinear error-correction," Journal of Econometrics, Elsevier, vol. 158(1), pages 78-94, September.
    11. Jiayue Zhang & Fukang Zhu & Huaping Chen, 2023. "Two-Threshold-Variable Integer-Valued Autoregressive Model," Mathematics, MDPI, vol. 11(16), pages 1-20, August.
    12. Drost, Feike C. & van den Akker, Ramon & Werker, Bas J.M., 2008. "Note on integer-valued bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 992-996, June.
    13. Muhammed Rasheed Irshad & Christophe Chesneau & Veena D’cruz & Naushad Mamode Khan & Radhakumari Maya, 2022. "Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    14. Barczy, M. & Ispány, M. & Pap, G., 2011. "Asymptotic behavior of unstable INAR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 583-608, March.
    15. Baena-Mirabete, S. & Puig, P., 2020. "Computing probabilities of integer-valued random variables by recurrence relations," Statistics & Probability Letters, Elsevier, vol. 161(C).
    16. Aknouche, Abdelhakim & Scotto, Manuel, 2022. "A multiplicative thinning-based integer-valued GARCH model," MPRA Paper 112475, University Library of Munich, Germany.
    17. 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.
    18. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
    19. Leisen, Fabrizio & Mena, Ramsés H. & Palma, Freddy & Rossini, Luca, 2019. "On a flexible construction of a negative binomial model," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 1-8.
    20. Vladica S. Stojanović & Hassan S. Bakouch & Eugen Ljajko & Najla Qarmalah, 2023. "Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    21. Federico Bassetti & Giulia Carallo & Roberto Casarin, 2022. "First-order integer-valued autoregressive processes with Generalized Katz innovations," Papers 2202.02029, arXiv.org.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

    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:bla:jtsera:v:29:y:2008:i:5:p:783-801. 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://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.