  The Lasso is a popular model selection and estimation procedure for linear
models that enjoys nice theoretical properties. In this paper, we study the
Lasso estimator for fitting autoregressive time series models. We adopt a
double asymptotic framework where the maximal lag may increase with the sample
size. We derive theoretical results establishing various types of consistency.
In particular, we derive conditions under which the Lasso estimator for the
autoregressive coefficients is model selection consistent, estimation
consistent and prediction consistent. Simulation study results are reported.
