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Semiparametric estimation of INAR models using roughness penalization

Author

Listed:
  • Maxime Faymonville

    (TU Dortmund University)

  • Carsten Jentsch

    (TU Dortmund University)

  • Christian H. Weiß

    (Helmut-Schmidt-University)

  • Boris Aleksandrov

    (Helmut-Schmidt-University)

Abstract

Popular models for time series of count data are integer-valued autoregressive (INAR) models, for which the literature mainly deals with parametric estimation. In this regard, a semiparametric estimation approach is a remarkable exception which allows for estimation of the INAR models without any parametric assumption on the innovation distribution. However, for small sample sizes, the estimation performance of this semiparametric estimation approach may be inferior. Therefore, to improve the estimation accuracy, we propose a penalized version of the semiparametric estimation approach, which exploits the fact that the innovation distribution is often considered to be smooth, i.e. two consecutive entries of the PMF differ only slightly from each other. This is the case, for example, in the frequently used INAR models with Poisson, negative binomially or geometrically distributed innovations. For the data-driven selection of the penalization parameter, we propose two algorithms and evaluate their performance. In Monte Carlo simulations, we illustrate the superiority of the proposed penalized estimation approach and argue that a combination of penalized and unpenalized estimation approaches results in overall best INAR model fits.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:stmapp:v:32:y:2023:i:2:d:10.1007_s10260-022-00655-0
    DOI: 10.1007/s10260-022-00655-0
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    References listed on IDEAS

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    1. Hee-Young Kim & Yousung Park, 2008. "A non-stationary integer-valued autoregressive model," Statistical Papers, Springer, vol. 49(3), pages 485-502, July.
    2. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
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    5. Annika Homburg & Christian H. Weiß & Gabriel Frahm & Layth C. Alwan & Rainer Göb, 2021. "Analysis and Forecasting of Risk in Count Processes," JRFM, MDPI, vol. 14(4), pages 1-25, April.
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    8. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
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    Cited by:

    1. Weiß, Christian H. & Zhu, Fukang, 2024. "Conditional-mean multiplicative operator models for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).

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