Estimating High-Dimensional Time Series Models

We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse,

high-dimensional, linear time-series models. We assume both the number of covariates in the

model and candidate variables can increase with the number of observations and the number of

candidate variables is, possibly, larger than the number of observations. We show the adaLASSO

consistently chooses the relevant variables as the number of observations increases (model selection

consistency,0), and has the oracle property, even when the errors are non-Gaussian and conditionally

heteroskedastic. A simulation study shows the method performs well in very general

settings. Finally, we consider two applications: in the first one the goal is to forecast quarterly

US inflation one-step ahead, and in the second we are interested in the excess return of the S&P

500 index. The method used outperforms the usual benchmarks in the literature.