# Variable selection in sparse high-dimensional GLARMA models

## TL;DR

This paper introduces a new variable selection method for high-dimensional GLARMA models that combines ARMA coefficient estimation with regularized GLM techniques, demonstrating improved accuracy and efficiency.

## Contribution

It presents a novel approach integrating ARMA coefficient estimation with regularized GLM methods for sparse high-dimensional models, with proven consistency and low computational load.

## Key findings

- Enhanced variable selection accuracy compared to existing methods
- Method shows low computational complexity and high efficiency
- Numerical experiments confirm improved performance on synthetic data

## Abstract

In this paper, we propose a novel variable selection approach in the framework of sparse high-dimensional GLARMA models. It consists in combining the estimation of the autoregressive moving average (ARMA) coefficients of these models with regularized methods designed for Generalized Linear Models (GLM). The properties of our approach are investigated both from a theoretical and a numerical point of view. More precisely, we establish in a specific case the consistency of the ARMA part coefficient estimators. We explain how to implement our approach and we show that it is very attractive since it benefits from a low computational load. We also assess the performance of our methodology using synthetic data and compare it with alternative approaches. Our numerical experiments show that combining the estimation of the ARMA part coefficients with regularized methods designed for GLM dramatically improves the variable selection performance.