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Asymptotic distribution of the Yule-Walker estimator for INAR(p) processes

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  • Silva, Isabel
  • Silva, M. Eduarda

Abstract

The INteger-valued AutoRegressive (INAR) processes were introduced in the literature by Al-Osh and Alzaid [1987. First-order integer-valued autoregressive (INAR(1)) process. J. Time Ser. Anal. 8, 261-275] and McKenzie [1988. Some ARMA models for dependent sequences of Poisson counts. Adv. Appl. Probab. 20, 822-835] for modelling correlated series of counts. These processes have been considered as the discrete counter part of AR processes, but their highly nonlinear characteristics lead to some statistically challenging problems, namely in parameter estimation. Several estimation procedures have been proposed in the literature, mainly for processes of first order. For some of these estimators the asymptotic properties as well as finite sample properties have been obtained and studied. This paper considers Yule-Walker parameter estimation for the pth-order integer-valued autoregressive, INAR(p), process. In particular, the asymptotic distribution of the Yule-Walker estimator is obtained and it is shown that this estimator is asymptotically normally distributed, unbiased and consistent.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:15:p:1655-1663
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    References listed on IDEAS

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    1. Maria Eduarda Silva & Vera Lúcia 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.
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    Cited by:

    1. Vladica S. Stojanović & Hassan S. Bakouch & Eugen Ljajko & Najla Qarmalah, 2023. "Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    2. Jentsch, Carsten & Weiß, Christian, 2017. "Bootstrapping INAR models," Working Papers 17-02, University of Mannheim, Department of Economics.
    3. Chen Xi & Wang Lihong, 2013. "Conditional L1 estimation for random coefficient integer-valued autoregressive processes," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 221-235, August.
    4. van den Akker, R., 2007. "Integer-valued time series," Other publications TiSEM e7f68743-db57-4056-9ca7-1, Tilburg University, School of Economics and Management.
    5. Kokoreva, Maria S. (Кокорева, Мария) & Stepanova, Anastasia N. (Степанова, Анастасия) & Karnoukhova, Elena V. (Карноухова, Елена), 2016. "What We Do not Know about the Ownership Structure of the Largest U.S. Companies? [Чего Мы Не Знаем О Структуре Собственности Крупнейших Компаний Сша?]," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 36-59, December.
    6. Marcelo Bourguignon, 2016. "Poisson–geometric INAR(1) process for modeling count time series with overdispersion," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(3), pages 176-192, August.
    7. 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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