IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i3p583-608.html
   My bibliography  Save this article

Asymptotic behavior of unstable INAR(p) processes

Author

Listed:
  • Barczy, M.
  • Ispány, M.
  • Pap, G.

Abstract

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unstable autoregressive processes of order p. An application for Boston armed robberies data set is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:3:p:583-608
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00263-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Víctor Enciso‐Mora & Peter Neal & T. Subba Rao, 2009. "Efficient order selection algorithms for integer‐valued ARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 1-18, January.
    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. Stuart Jay Deutsch & Francis B. Alt, 1977. "The Effect of Massachusetts' Gun Control Law On Gun-Related Crimes in the City of Boston," Evaluation Review, , vol. 1(4), pages 543-568, November.
    4. Richard A. Hay JR & Richard McCleary, 1979. "Box-Tiao Time Series Models for Impact Assessment," Evaluation Review, , vol. 3(2), pages 277-314, May.
    5. 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.
    6. 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.
    7. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    8. Brendan P.M. McCabe & Gael M. Martin & David Harris, 2009. "Optimal Probabilistic Forecasts for Counts," Monash Econometrics and Business Statistics Working Papers 7/09, Monash University, Department of Econometrics and Business Statistics.
    9. Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(3), pages 269-306, September.
    10. repec:bla:jecsur:v:12:y:1998:i:5:p:423-69 is not listed on IDEAS
    11. repec:tiu:tiutis:6b90fe6f-4de9-4192-9f4d-99ae9220af75 is not listed on IDEAS
    12. 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.
    13. Wei, C. Z. & Winnicki, J., 1989. "Some asymptotic results for the branching process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 261-282, April.
    14. van der Meer, Tjacco & Pap, Gyula & van Zuijlen, Martien C.A., 1999. "ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES," Econometric Theory, Cambridge University Press, vol. 15(2), pages 184-217, April.
    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. Barczy, Mátyás & Körmendi, Kristóf & Pap, Gyula, 2015. "Statistical inference for 2-type doubly symmetric critical irreducible continuous state and continuous time branching processes with immigration," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 92-123.
    2. Kristóf Körmendi & Gyula Pap, 2018. "Statistical inference of 2-type critical Galton–Watson processes with immigration," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 169-190, April.
    3. Barczy, Mátyás & Bezdány, Dániel & Pap, Gyula, 2023. "Asymptotic behaviour of critical decomposable 2-type Galton–Watson processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 318-350.
    4. 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.

    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. Ling, Shiqing & McAleer, Michael, 2004. "Regression quantiles for unstable autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 304-328, May.
    2. 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.
    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. 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.
    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. Ploberger, Werner, 2004. "A complete class of tests when the likelihood is locally asymptotically quadratic," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 67-94.
    7. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.
    8. 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.
    9. Castro, Tomás del Barrio & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2013. "The Impact Of Persistent Cycles On Zero Frequency Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1289-1313, December.
    10. 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.
    11. Schatz, Michael & Wheatley, Spencer & Sornette, Didier, 2022. "The ARMA Point Process and its Estimation," Econometrics and Statistics, Elsevier, vol. 24(C), pages 164-182.
    12. Buchmann, Boris & Chan, Ngai Hang, 2013. "Unified asymptotic theory for nearly unstable AR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 952-985.
    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. Ventosa-Santaularària, Daniel & Gómez, Manuel, 2006. "Inflation and Breaks: the validity of the Dickey-Fuller test," MPRA Paper 58773, University Library of Munich, Germany.
    15. Kachour Maher & Bakouch Hassan S. & Mohammadi Zohreh, 2023. "A New INAR(1) Model for ℤ-Valued Time Series Using the Relative Binomial Thinning Operator," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 243(2), pages 125-152, April.
    16. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Maximum Likelihood Estimation in Panels with Incidental Trends," Cowles Foundation Discussion Papers 1246, Cowles Foundation for Research in Economics, Yale University.
    17. Werner Ploberger & Peter C.B. Phillips, 1998. "Rissanen's Theorem and Econometric Time Series," Cowles Foundation Discussion Papers 1197, Cowles Foundation for Research in Economics, Yale University.
    18. John Geweke & Joel Horowitz & M. Hashem Pesaran, 2006. "Econometrics: A Bird’s Eye View," CESifo Working Paper Series 1870, CESifo.
    19. Christian Weiss, 2009. "Monitoring correlated processes with binomial marginals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(4), pages 399-414.
    20. Michael Jansson & Morten Ørregaard Nielsen, 2012. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 80(5), pages 2321-2332, 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:eee:spapps:v:121:y:2011:i:3:p:583-608. 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.