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.