L_1-Regularization of High-Dimensional Time-Series Models with Flexible Innovations

Abstract

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.

Real-time inflation forecasting with high-dimensional models: The case of Brazil

“…Medeiros and Mendes (2016) showed that the conditions that must be satisfied on the adaLASSO are very general. The model works even when the number of variables increases faster than the number of observations and when the errors are non-Gaussian and heteroskedastic.…”

Machine learning and oil price point and density forecasting

“…In general, is set to unity and b j is estimated in the …rst-step using LASSO. According to Medeiros and Mendes (2016), the conditions required by the adalasso estimator are very general and the model works even when the errors are non-Gaussian, heteroskedastic and the number of variables increases faster than the number of observations. Model 10 (Ridge regression): It is well known OLS often does poorly in prediction on future data (e.g., due to over…tting).…”

Forecasting Brazilian Inflation with High-Dimensional Models

“…framework may be complicated. Moreover, Medeiros and Mendes (2015) showed that selecting the parameters λ and τ in a time-series environment by using the BIC and the LASSO as the first step for the adaLASSO yields estimates that have the oracle property even in adverse situations with heteroskedasticity and t distributed errors. Moreover, the authors allow the number of candidate variables to increase with the number of observations and show that, based on these conditions, the adaLASSO has model selection consistency, i.e., it chooses the most parsimonious model asymptotically.…”