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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

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. Copyright (c) 2009 Royal Statistical Society.

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.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:2:p:467-485
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    References listed on IDEAS

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    1. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
    2. Silva, Isabel & Silva, M. Eduarda, 2006. "Asymptotic distribution of the Yule-Walker estimator for INAR(p) processes," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1655-1663, September.
    3. Keith Freeland, R. & McCabe, Brendan, 2005. "Asymptotic properties of CLS estimators in the Poisson AR(1) model," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 147-153, June.
    4. 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.
    5. Maria Eduarda Silva & Vera Lucia 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Jentsch, Carsten & Leucht, Anne, 2014. "Bootstrapping Sample Quantiles of Discrete Data," Working Papers 14-15, University of Mannheim, Department of Economics.
    4. Tianqing Liu & Xiaohui Yuan, 2013. "Random rounded integer-valued autoregressive conditional heteroskedastic process," Statistical Papers, Springer, vol. 54(3), pages 645-683, August.
    5. 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.
    6. 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.
    7. David T. Frazier & Worapree Maneesoonthorn & Gael M. Martin & Brendan P.M. McCabe, 2018. "Approximate Bayesian forecasting," Monash Econometrics and Business Statistics Working Papers 2/18, Monash University, Department of Econometrics and Business Statistics.
    8. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
    9. Carsten Jentsch & Anne Leucht, 2016. "Bootstrapping sample quantiles of discrete data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(3), pages 491-539, June.
    10. 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.

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