Parametric or nonparametric: the FIC approach for stationary time series

TL;DR

This paper introduces a new focused information criterion (FIC) for stationary time series that compares parametric and nonparametric models based on mean squared error of estimators for specific parameters, aiding model selection.

Contribution

It develops a generalized FIC framework for directly comparing parametric and nonparametric models for targeted parameters in stationary time series.

Findings

FIC formulas for covariances and correlations at specific lags

AFIC provides model selection strategies for estimating sequences of parameters

The approach narrows the gap between parametric and nonparametric modeling

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.