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The focussed information criterion for generalised linear regression models for time series

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  • S. C. Pandhare
  • T. V. Ramanathan

Abstract

The present paper proposes the focussed information criterion (FIC) to tackle the model selection problems pertinent to generalised linear models (GLM) for time series. As a first step towards constructing the FIC, we formally discuss the local asymptotic theory of quasi‐maximum likelihood estimation for time series GLM under potential model misspecification. The general FIC formula is derived subsequently that is useful for the simultaneous selection of the order of the autoregressive response as well as a subset of important covariates. We also develop the average FIC (AFIC) that is instrumental in selecting an overall good model for a range of covariates and time regions and establish the equivalence of the AFIC with the classical Akaike's information criterion (AIC). We demonstrate our theory with the analysis of rainfall patterns in Melbourne by means of the logistic and Gamma regression models.

Suggested Citation

  • S. C. Pandhare & T. V. Ramanathan, 2020. "The focussed information criterion for generalised linear regression models for time series," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 485-507, December.
    • Handle: RePEc:bla:anzsta:v:62:y:2020:i:4:p:485-507
    DOI: 10.1111/anzs.12310
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    References listed on IDEAS

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    1. Gerda Claeskens & Christophe Croux & Johan Van Kerckhoven, 2006. "Variable Selection for Logistic Regression Using a Prediction-Focused Information Criterion," Biometrics, The International Biometric Society, vol. 62(4), pages 972-979, December.
    2. Hansen, Bruce E., 2005. "Challenges For Econometric Model Selection," Econometric Theory, Cambridge University Press, vol. 21(1), pages 60-68, February.
    3. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, October.
    4. Pircalabelu, Eugen & Claeskens, Gerda & Waldorp, Lourens J., 2015. "A focused information criterion for graphical models," LIDAM Reprints ISBA 2015044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Gerda Claeskens & Raymond J. Carroll, 2007. "An asymptotic theory for model selection inference in general semiparametric problems," Biometrika, Biometrika Trust, vol. 94(2), pages 249-265.
    6. Gerda Claeskens, 2012. "Focused estimation and model averaging with penalization methods: an overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 272-287, August.
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