#### ℓ1-Regularization of high-dimensional time-series models with flexible innovations

TD n. 636, 13/04/2015

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

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

model and the number of candidate variables can increase with the sample size (polynomially or

geometrically). In other words, we let the number of candidate variables to be larger than the

number of observations. We show the adaLASSO consistently chooses the relevant variables as the

number of observations increases (model selection consistency) and has the oracle property, even

when the errors are non-Gaussian and conditionally heteroskedastic. This allows the adaLASSO

to be applied to a myriad of applications in empirical finance and macroeconomics. A simulation

study shows that the method performs well in very general settings with t-distributed and heteroskedastic

errors as well with highly correlated regressors. Finally, we consider an application to

forecast monthly US inflation with many predictors. The model estimated by the adaLASSO delivers

superior forecasts than traditional benchmark competitors such as autoregressive and factor

models.

Marcelo Medeiros, Eduardo F. Mendes.