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Generalized Integer-Valued Autoregression

Author

Listed:
  • Brännäs, Kurt

    (Department of Economics, Umeå University)

  • Hellström, Jörgen

    (Department of Economics, Umeå University)

Abstract

The integer-valued AR(1) model is generalized to encompass some of the more likely features of economic time series of count data. The generalizations come at the price of loosing exact distributional properties. For most specifications the first and second order both conditional and unconditional moments can be obtained. Hence estimation, testing and forecasting are feasible and can be based on least squares or GMM techniques. An illustration based on the number of plants within an industrial sector is considered.

Suggested Citation

  • Brännäs, Kurt & Hellström, Jörgen, 1999. "Generalized Integer-Valued Autoregression," Umeå Economic Studies 501, Umeå University, Department of Economics.
  • Handle: RePEc:hhs:umnees:0501
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    Cited by:

    1. Daunfeldt, Sven-Olov & Orth, Matilda & Rudholm, Niklas, 2008. "Does the Quality of Store Brands Affect the Number of National Brand Suppliers?," HUI Working Papers 18, HUI Research.
    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. David M. Waguespack & Robert Salomon, 2016. "Quality, Subjectivity, and Sustained Superior Performance at the Olympic Games," Management Science, INFORMS, vol. 62(1), pages 286-300, January.
    4. 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.
    5. Hellström, Jörgen & Simonsen, Ola, 2006. "Does the Open Limit Order Book Reveal Information About Short-run Stock Price Movements?," Umeå Economic Studies 687, Umeå University, Department of Economics.
    6. 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.
    7. Brannas, Kurt & Hellstrom, Jorgen & Nordstrom, Jonas, 2002. "A new approach to modelling and forecasting monthly guest nights in hotels," International Journal of Forecasting, Elsevier, vol. 18(1), pages 19-30.
    8. 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.
    9. Hellstrom, Jorgen, 2001. "Unit root testing in integer-valued AR(1) models," Economics Letters, Elsevier, vol. 70(1), pages 9-14, January.
    10. 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.
    11. Jung, Robert C. & Tremayne, A.R., 2006. "Coherent forecasting in integer time series models," International Journal of Forecasting, Elsevier, vol. 22(2), pages 223-238.
    12. Maxime Faymonville & Carsten Jentsch & Christian H. Weiß & Boris Aleksandrov, 2023. "Semiparametric estimation of INAR models using roughness penalization," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 365-400, June.
    13. 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.
    14. Andersson, Jonas & Karlis, Dimitris, 2008. "Treating missing values in INAR(1) models," Discussion Papers 2008/14, Norwegian School of Economics, Department of Business and Management Science.
    15. Aliou DIAGNE, 2006. "Diffusion And Adoption Of Nerica Rice Varieties In Côte D’Ivoire," The Developing Economies, Institute of Developing Economies, vol. 44(2), pages 208-231, June.
    16. Robert Jung & Gerd Ronning & A. Tremayne, 2005. "Estimation in conditional first order autoregression with discrete support," Statistical Papers, Springer, vol. 46(2), pages 195-224, April.

    More about this item

    Keywords

    Characterization; Dependence; Time series model; Estimation; Forecasting; Entry and exit;
    All these keywords.

    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
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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