Parametric or nonparametric: the FIC approach for stationary time series
Abstract
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.
Cite
@article{arxiv.2602.17261,
title = {Parametric or nonparametric: the FIC approach for stationary time series},
author = {Gudmund Hermansen and Nils Lid Hjort and Martin Jullum},
journal= {arXiv preprint arXiv:2602.17261},
year = {2026}
}
Comments
21 pages, 6 figures; Statistical Research Report (Department of Mathematics, University of Oslo), from December 2015, but arXiv'd February 2026; a later modified and extended version might then become a journal paper