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Partial Likelihood Inference For Time Series Following Generalized Linear Models

Author

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  • Konstantinos Fokianos
  • Benjamin Kedem

Abstract

. The present article offers a certain unifying approach to time series regression modelling by combining partial likelihood (PL) inference and generalized linear models. An advantage gained by resorting to PL is that the joint distribution of the response and the covariates is left unspecified, and furthermore, PL allows for temporal or sequential conditional inference with respect to a filtration generated by all that is known to the observer at the time of observation. Two real data examples illustrate the methodology.

Suggested Citation

  • Konstantinos Fokianos & Benjamin Kedem, 2004. "Partial Likelihood Inference For Time Series Following Generalized Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 173-197, March.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:2:p:173-197
    DOI: 10.1046/j.0143-9782.2003.00344.x
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    References listed on IDEAS

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    2. Konstantinos Fokianos, 2001. "Truncated Poisson Regression for Time Series of Counts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 645-659, December.
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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. Guilherme Pumi & Taiane Schaedler Prass & Rafael Rigão Souza, 2021. "A dynamic model for double‐bounded time series with chaotic‐driven conditional averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 68-86, March.
    3. Klingenberg, Bernhard, 2008. "Regression models for binary time series with gaps," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4076-4090, April.
    4. Rongning Wu & Yunwei Cui, 2014. "A Parameter-Driven Logit Regression Model For Binary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 462-477, August.
    5. Taiane Schaedler Prass & Guilherme Pumi & Cleiton Guollo Taufemback & Jonas Hendler Carlos, 2025. "Positive time series regression models: theoretical and computational aspects," Computational Statistics, Springer, vol. 40(3), pages 1185-1215, March.
    6. Farouk Mselmi & Célestin C. Kokonendji, 2025. "Multivariate generalized linear models for Markov kernels with (un)known link and variance functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(4), pages 896-926, December.
    7. Singh, Rakhi & Mukhopadhyay, Siuli, 2019. "Exact Bayesian designs for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 157-170.
    8. Guilherme Pumi & Danilo Hiroshi Matsuoka & Taiane Schaedler Prass & Bruna Gregory Palm, 2026. "A Matsuoka‐Based GARMA Model for Environmental and Energy Systems: Theory, Estimation, and Applications," Environmetrics, John Wiley & Sons, Ltd., vol. 37(3), April.
    9. R. Prabhakar Rao & Brajendra C. Sutradhar, 2020. "Multiple Categorical Covariates-Based Multinomial Dynamic Response Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 186-219, February.
    10. Konstantinos Fokianos & Roland Fried, 2010. "Interventions in INGARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 210-225, May.
    11. Andréa Rocha & Francisco Cribari-Neto, 2009. "Beta autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 529-545, November.
    12. Mirko Armillotta & Konstantinos Fokianos, 2024. "Count network autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(4), pages 584-612, July.
    13. Fokianos, Konstantions & Fried, Roland, 2009. "Interventions in ingarch processes," Technical Reports 2009,11, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Luis E. Nieto-Barajas, 2022. "Dependence on a collection of Poisson random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 21-39, March.
    15. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    16. Guilherme Pumi & Taiane Schaedler Prass & Cleiton Guollo Taufemback, 2024. "Publisher Correction: Unit-Weibull autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 358-359, March.
    17. Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
    18. Marinho G. Andrade & Katiane S. Conceição & Nalini Ravishanker, 2024. "Zero-modified count time series modeling with an application to influenza cases," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 611-637, September.
    19. Brajendra C. Sutradhar & Asokan M. Variyath, 2020. "A New Look at the Models for Ordinal Categorical Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 111-141, May.
    20. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
    21. Vurukonda Sathish & Siuli Mukhopadhyay & Rashmi Tiwari, 2022. "Autoregressive and moving average models for zero‐inflated count time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(2), pages 190-218, May.
    22. Kleber H. Santos & Francisco Cribari‐Neto, 2024. "A Varying Precision Beta Prime Autoregressive Moving Average Model With Application to Water Flow Data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(8), December.
    23. Wenqing Li & Chuhan Yang & Saif Eddin Jabari, 2022. "Nonlinear Traffic Prediction as a Matrix Completion Problem with Ensemble Learning," Transportation Science, INFORMS, vol. 56(1), pages 52-78, January.
    24. Moizes Melo & Airlane Alencar, 2020. "Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 830-857, November.

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