Variable selection in sparse GLARMA models

• Published in: Statistics (Berlin, DDR) Vol. 56; no. 4; pp. 755 - 784
• Main Authors: Gomtsyan, Marina, Lévy-Leduc, Céline, Ouadah, Sarah, Sansonnet, Laure, Blein, Thomas
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.07.2022; Taylor & Francis Ltd; Taylor & Francis: STM, Behavioural Science and Public Health Titles
• Subjects: Autoregressive moving-average models; discrete-valued time series; GLARMA models; Methodology; Regression coefficients; sparse; Statistical models; Statistics; GLARMA models; sparse; discrete-valued time series
• ISSN: 0233-1888; 1029-4910
• DOI: 10.1080/02331888.2022.2090943

In this paper, we propose a novel and efficient two-stage variable selection approach for sparse GLARMA models, which are pervasive for modelling discrete-valued time series. Our approach consists in iteratively combining the estimation of the autoregressive moving average (ARMA) coefficients of GLARMA models with regularized methods designed for performing variable selection in regression coefficients of Generalized Linear Models (GLM). We first establish the consistency of the ARMA part coefficient estimators in a specific case. Then, we explain how to efficiently implement our approach. Finally, we assess the performance of our methodology using synthetic data, compare it with alternative methods and illustrate it on an example of real-world application. Our approach, which is implemented in the GlarmaVarSel R package, is very attractive since it benefits from a low computational load and is able to outperform the other methods in terms of recovering the non-null regression coefficients.