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

We propose an iterative variable selection approach in multivariate sparse GLARMA models for modeling multivariate discrete-valued time series. The estimation in our approach is performed in two steps: firstly, our approach estimates the autoregressive moving average (ARMA) coefficients of multivariate GLARMA models, followed by variable selection in the coefficients of the Generalized Linear Model using regularized methods. We provide a detailed description of the implementation of our approach. Subsequently, we study its performance on simulated data and compare it with other methods. Finally, we illustrate its application on RNA-Seq data resulting from polyribosome profiling to determine translational status for all mRNAs in germinating seeds. The proposed approach benefits from a number of attractive features: it has a low computational load and outperforms other methods in accurately performing variable selection and, consequently, recovering the null and non-null coefficients. Furthermore, being implemented in the MultiGlarmaVarSel R package and openly accessible on the CRAN, our variable selection method holds significant appeal for broader applications across diverse scientific disciplines.