Vector autoregressive models have had a considerable impact in macroeconomics and the world of finance, as it provides an appealing way of modelling spatio-temporal relationships between a number of time series. There has also been attempts to model the evolution of a time series over time in the presence of exogenous predictors,in particular, the study of VAR-X models, where the response depends on its past values as well as current and past values of an exogenous predictor. However, VAR models tend to suffer from having a relatively large number of parameters,especially when available data are scarce. To overcome the problem of high dimensions, we assume the underlying model is sparse and propose to estimate the parameters consistency using the well known lasso technique. We examine how the temporal and cross sectional dependencies inherent in the model,affects the lasso estimator, and give theoretical guarantees for its convergence.