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Likelihood Inference for Generalized Integer Autoregressive Time Series Models

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  • Harry Joe

    (Department of Statistics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada)

Abstract

For modeling count time series data, one class of models is generalized integer autoregressive of order p based on thinning operators. It is shown how numerical maximum likelihood estimation is possible by inverting the probability generating function of the conditional distribution of an observation given the past p observations. Two data examples are included and show that thinning operators based on compounding can substantially improve the model fit compared with the commonly used binomial thinning operator.

Suggested Citation

  • Harry Joe, 2019. "Likelihood Inference for Generalized Integer Autoregressive Time Series Models," Econometrics, MDPI, vol. 7(4), pages 1-13, October.
    • Handle: RePEc:gam:jecnmx:v:7:y:2019:i:4:p:43-:d:275407
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    References listed on IDEAS

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    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004. "Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks," Umeå Economic Studies 637, Umeå University, Department of Economics.
    3. Du Jin‐Guan & Li Yuan, 1991. "THE INTEGER‐VALUED AUTOREGRESSIVE (INAR(p)) MODEL," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(2), pages 129-142, March.
    4. A. Alzaid & M. Al-Osh, 1993. "Some autoregressive moving average processes with generalized Poisson marginal distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 223-232, June.
    5. Xanthi Pedeli & Anthony C. Davison & Konstantinos Fokianos, 2015. "Likelihood Estimation for the INAR( p ) Model by Saddlepoint Approximation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1229-1238, September.
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