ℓ1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors

Resumo

We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. The adaLASSO is a one-step implementation of the family of folded concave penalized least-squares. 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.

Ficha do documento

Tipo

Artigo científico

Ano

2016

Instituição

Elsevier Ltd

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Acesso restrito

DOI

10.1016/j.jeconom.2015.10.011

Identificador

oai:repositorio.fgv.br:10438/23546

Temas

Modelagem EconômicaDados

Palavras-chave

EconomicsGaussian Noise (Electronic)Time seriesAsymptotic propertiesHighly-correlatedLinear time series modelModel selection consistenciesPenalized least-squaresSimulation studiesTime series modelsSparse modelsShrinkageLASSOAdaLASSOGARCHPropriedades assintóticasModelo linear de séries temporaisMatemáticaAnálise de séries temporaisModelagem de dados