  Time series of counts occurring in various applications are often
overdispersed, meaning their variance is much larger than the mean. This paper
proposes a novel variable selection approach for processing such data. Our
approach consists in modelling them using sparse negative binomial GLARMA
models. It combines estimating the autoregressive moving average (ARMA)
coefficients of GLARMA models and the overdispersion parameter with performing
variable selection in regression coefficients of Generalized Linear Models
(GLM) with regularised methods. We describe our three-step estimation
procedure, which is implemented in the NBtsVarSel package. We evaluate the
performance of the approach on synthetic data and compare it to other methods.
Additionally, we apply our approach to RNA sequencing data. Our approach is
computationally efficient and outperforms other methods in selecting variables,
i.e. recovering the non-null regression coefficients.
