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We propose a novel and efficient iterative two-stage variable selectionapproach for multivariate sparse GLARMA models, which can be used for modellingmultivariate discrete-valued time series. Our approach consists in iterativelycombining two steps: the estimation of the autoregressive moving average (ARMA)coefficients of multivariate GLARMA models and the variable selection in thecoefficients of the Generalized Linear Model (GLM) part of the model performedby regularized methods. We explain how to implement our approach efficiently.Then we assess the performance of our methodology using synthetic data andcompare it with alternative methods. Finally, we illustrate it on RNA-Seq dataresulting from polyribosome profiling to determine translational status for allmRNAs in germinating seeds. Our approach, which is implemented in theMultiGlarmaVarSel R package and available on the CRAN, is very attractive sinceit benefits from a low computational load and is able to outperform the othermethods for recovering the null and non-null coefficients.

Variable selection in sparse multivariate GLARMA models: Application to germination control by environment