DATA DRIVEN MODEL SELECTION FOR SAME-REALIZATION PREDICTIONS IN AUTOREGRESSIVE PROCESSES

Kare Kamila (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

This paper is about the one-step ahead prediction of the future of observations drawn from an infinite-order autoregressive AR($\infty$) process. It aims to design penalties (fully data driven) ensuring that the selected model verifies the efficiency property but in the non asymptotic framework. We show that the excess risk of the selected estimator enjoys the best bias-variance trade-off over the considered collection. %with the leading constant almost one. To achieve these results, we needed to overcome the dependence difficulties by following a classical approach which consists in restricting to a set where the empirical covariance matrix is equivalent to the theoretical one. We show that this event happens with probability larger than $1-c_0/n^2$ with $c_0>0$. The proposed data driven criteria are based on the minimization of the penalized criterion akin to the Mallows's $C_p$.

Mots clés: Model selection; oracle inequality; efficiency; autoregressive process; data driven

Domaines: Machine Learning [stat.ML]; Théorie [stat.TH]

Kare Kamila. DATA DRIVEN MODEL SELECTION FOR SAME-REALIZATION PREDICTIONS IN AUTOREGRESSIVE PROCESSES. 2022. ⟨hal-03169343v2⟩