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.

中文翻译：

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时间序列广义线性回归模型的集中信息准则

本文提出了聚焦信息准则（FIC）来解决与时间序列的广义线性模型（GLM）有关的模型选择问题。作为构建FIC的第一步，我们正式讨论了潜在模型错误指定下时间序列GLM的拟最大似然估计的局部渐近理论。随后得出一般的FIC公式，该公式可用于同时选择自回归响应的阶数以及重要协变量的子集。我们还开发了平均FIC（AFIC），它有助于为一系列协变量和时区选择总体良好的模型，并建立与经典Akaike信息标准（AIC）等效的AFIC。