Penalised inference for lagged dependent regression in the presence of autocorrelated residuals

This paper deals with linear models for a time-dependent response and explanatory variables in a high-dimensional setting. We account for the time dependency in the data by explicitly adding autoregressive terms to the response variable in the model together with an autoregressive process for the residuals. We present a penalized likelihood approach for parameter estimation and discuss its theoretical properties. Finally, we show the successful application of the proposed methodology on simulated data and on two real applications, where we model air pollution and stock market indices, respectively. We provide an implementation of the method in the R package DREGAR, freely available on CRAN, http://CRAN.R-project.org/package=DREGAR.