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Testing for serial dependence in time series models of counts

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  • Robert C. Jung
  • A. R. Tremayne

Abstract

. In analysing time series of counts, the need to test for the presence of a dependence structure routinely arises. Suitable tests for this purpose are considered in this paper. Their size and power properties are evaluated under various alternatives taken from the class of INARMA processes. We find that all the tests considered except one are robust against extra binomial variation in the data and that tests based on the sample autocorrelations and the sample partial autocorrelations can help to distinguish between integer‐valued first‐order and second‐order autoregressive as well as first‐order moving average processes.

Suggested Citation

  • Robert C. Jung & A. R. Tremayne, 2003. "Testing for serial dependence in time series models of counts," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 65-84, January.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:1:p:65-84
    DOI: 10.1111/1467-9892.00293
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    References listed on IDEAS

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    1. D. S. Poskitt & A. R. Tremayne, 1986. "Some Aspects Of The Performance Of Diagnostic Checks In Bivariate Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 217-233, May.
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    Cited by:

    1. 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.
    2. Alfredo García-Hiernaux, 2009. "Diagnostic checking using subspace methods," Documentos de Trabajo del ICAE 2009-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Masoomeh Forughi & Zohreh Shishebor & Atefeh Zamani, 2022. "Portmanteau tests for generalized integer-valued autoregressive time series models," Statistical Papers, Springer, vol. 63(4), pages 1163-1185, August.
    4. Khan Naushad Mamode & Sunecher Yuvraj & Jowaheer Vandna, 2017. "Analyzing the Full BINMA Time Series Process Using a Robust GQL Approach," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-12, July.
    5. Pedro H. C. Sant’Anna, 2017. "Testing for Uncorrelated Residuals in Dynamic Count Models With an Application to Corporate Bankruptcy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 349-358, July.
    6. Christian Weiß, 2015. "A Poisson INAR(1) model with serially dependent innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 829-851, October.
    7. 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.
    8. B.P.M. McCabe & G.M. Martin, 2003. "Coherent Predictions of Low Count Time Series," Monash Econometrics and Business Statistics Working Papers 8/03, Monash University, Department of Econometrics and Business Statistics.
    9. 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.
    10. 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.
    11. Franklin E. Zimring & Jeffrey Fagan & David T. Johnson, 2010. "Executions, Deterrence, and Homicide: A Tale of Two Cities," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 7(1), pages 1-29, March.
    12. Lucio Palazzo & Riccardo Ievoli, 2022. "A Semiparametric Approach to Test for the Presence of INAR: Simulations and Empirical Applications," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    13. 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.
    14. 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.
    15. 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.

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