We seek to narrow the gap between parametric and nonparametric modelling of stationary time series processes. The approach is inspired by recent advances in focused inference and model selection techniques. The paper generalises and extends recent work by developing a new version of the focused information criterion (FIC), directly comparing the performance of parametric time series models with a nonparametric alternative. For a pre-specified focused parameter, for which scrutiny is considered valuable, this is achieved by comparing the mean squared error of the model-based estimators of this quantity. In particular, this yields FIC formulae for covariances or correlations at specified lags, for the probability of reaching a threshold, etc. Suitable weighted average versions, the AFIC, also lead to model selection strategies for finding the best model for the purpose of estimating e.g.~a sequence of correlations.

翻译：本文旨在缩小平稳时间序列过程参数化建模与非参数化建模之间的差距。该方法受到聚焦推断与模型选择技术最新进展的启发。通过发展聚焦信息准则（FIC）的新版本，本文推广并扩展了近期研究成果，直接比较参数化时间序列模型与非参数替代模型的性能。针对预先指定的、被认为具有重要研究价值的聚焦参数，该方法通过比较基于不同模型的该参数估计量的均方误差来实现上述比较。特别地，该方法推导出特定滞后阶数的协方差或相关系数、达到阈值的概率等参数的FIC计算公式。通过构建合适的加权平均版本（AFIC），还可形成针对特定目标的模型选择策略，例如在估计相关系数序列时寻找最优模型。