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Locally asymptotically efficient estimation for parametric PINAR(p) models

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  • Mohamed Sadoun
  • Mohamed Bentarzi

Abstract

This article focuses on the efficient estimation problem of an arbitrary‐order periodic integer‐valued autoregressive (PINAR(p)) model. Both the local asymptotic normality (LAN) property and the local asymptotic linearity property satisfied by the central sequence of the underlying model are established. Using these results, we construct efficient estimators for the parameters in a parametric framework. The consistency property of these efficient estimations is evaluated via an intensive simulation study. Moreover, the performances of these efficient estimations, over the conditional maximum likelihood (CML) and the conditional least squares (CLS) estimations, are also illustrated via an intensive simulation study and an application on real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:3:p:257-289
    DOI: 10.1111/stan.12234
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    References listed on IDEAS

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    1. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    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. Rong Zhu & Harry Joe, 2006. "Modelling Count Data Time Series with Markov Processes Based on Binomial Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 725-738, September.
    4. 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.
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