Title: Desparsified lasso in time series
Authors: Robert Adamek - Maastricht University (Netherlands) [presenting]
Ines Wilms - Maastricht University (Netherlands)
Stephan Smeekes - Maastricht University (Netherlands)
Abstract: The Desparsified Lasso is a high-dimensional estimation method which provides uniformly valid inference. We extend this method to a time series setting under mixingale assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension. We first derive an oracle inequality for the (regular) Lasso, relaxing the commonly made exact sparsity assumption to a weaker alternative, which permits many small but non-zero coefficients. The weak sparsity coupled with the mixingale assumption means this inequality can also be applied to the (inherently misspecified) nodewise regressions performed in the Desparsified Lasso. This allows us to establish the uniform asymptotic normality of the Desparsified Lasso under general conditions. Additionally, we show consistency of a long-run variance estimator, thus providing a complete set of tools for performing inference in high-dimensional linear models. Finally, we perform a simulation exercise to demonstrate the small sample properties of the Desparsified Lasso in common time series settings.