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Asymptotic Behavior of Conditional Least Squares Estimators for Unstable Integer-valued Autoregressive Models of Order 2

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  • Mátyás Barczy
  • Márton Ispány
  • Gyula Pap

Abstract

type="main" xml:id="sjos12069-abs-0001"> In this paper, the asymptotic behavior of the conditional least squares estimators of the autoregressive parameters, of the mean of the innovations, and of the stability parameter for unstable integer-valued autoregressive processes of order 2 is described. The limit distributions and the scaling factors are different according to the following three cases: (i) decomposable, (ii) indecomposable but not positively regular, and (iii) positively regular models.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:866-892
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    File URL: http://hdl.handle.net/10.1111/sjos.12069
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    References listed on IDEAS

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    1. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    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. 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.
    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. 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.
    7. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    8. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
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    Cited by:

    1. Mátyás Barczy & Kristóf Körmendi & Gyula Pap, 2016. "Statistical inference for critical continuous state and continuous time branching processes with immigration," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 789-816, October.
    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. Mátyás Barczy & Zenghu Li & Gyula Pap, 2016. "Moment Formulas for Multitype Continuous State and Continuous Time Branching Process with Immigration," Journal of Theoretical Probability, Springer, vol. 29(3), pages 958-995, September.

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