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Efficient estimation of auto‐regression parameters and innovation distributions for semiparametric integer‐valued AR(p) models

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  • Feike C. Drost
  • Ramon van den Akker
  • Bas J. M. Werker

Abstract

Summary. Integer‐valued auto‐regressive (INAR) processes have been introduced to model non‐negative integer‐valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of auto‐regression coefficients and a probability distribution on the non‐negative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. The paper instead considers a more realistic semiparametric INAR(p) model where there are essentially no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of both the auto‐regression parameters and the innovation distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:2:p:467-485
    DOI: 10.1111/j.1467-9868.2008.00687.x
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    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. Weiß, Christian H. & Zhu, Fukang, 2024. "Conditional-mean multiplicative operator models for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    3. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    4. Raju Maiti & Atanu Biswas & Samarjit Das, 2016. "Coherent forecasting for count time series using Box–Jenkins's AR(p) model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(2), pages 123-145, May.
    5. 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.
    6. Jentsch, Carsten & Leucht, Anne, 2014. "Bootstrapping Sample Quantiles of Discrete Data," Working Papers 14-15, University of Mannheim, Department of Economics.
    7. Yao Rao & David Harris & Brendan McCabe, 2022. "A semi‐parametric integer‐valued autoregressive model with covariates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 495-516, June.
    8. Tianqing Liu & Xiaohui Yuan, 2013. "Random rounded integer-valued autoregressive conditional heteroskedastic process," Statistical Papers, Springer, vol. 54(3), pages 645-683, August.
    9. Frazier, David T. & Maneesoonthorn, Worapree & Martin, Gael M. & McCabe, Brendan P.M., 2019. "Approximate Bayesian forecasting," International Journal of Forecasting, Elsevier, vol. 35(2), pages 521-539.
    10. 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.
    11. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
    12. Germán Aneiros, 2012. "Comments on: 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 439-441, September.
    13. A. M. M. Shahiduzzaman Quoreshi & Reaz Uddin & Naushad Mamode Khan, 2019. "Quasi-Maximum Likelihood Estimation for Long Memory Stock Transaction Data—Under Conditional Heteroskedasticity Framework," JRFM, MDPI, vol. 12(2), pages 1-13, April.
    14. 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.
    15. Zeng, Xiaoqiang & Kakizawa, Yoshihide, 2022. "Bias-correction of some estimators in the INAR(1) process," Statistics & Probability Letters, Elsevier, vol. 187(C).
    16. Vance L. Martin & Andrew R. Tremayne & Robert C. Jung, 2014. "Efficient Method Of Moments Estimators For Integer Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 491-516, November.
    17. Jentsch, Carsten & Weiß, Christian, 2017. "Bootstrapping INAR models," Working Papers 17-02, University of Mannheim, Department of Economics.
    18. Robert C. Jung & Andrew R. Tremayne, 2020. "Maximum-Likelihood Estimation in a Special Integer Autoregressive Model," Econometrics, MDPI, vol. 8(2), pages 1-15, June.
    19. Luisa Bisaglia & Margherita Gerolimetto, 2019. "Model-based INAR bootstrap for forecasting INAR(p) models," Computational Statistics, Springer, vol. 34(4), pages 1815-1848, December.

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